filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Antichain.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.Preorder.Chain
/-!
# Antichains
This file defines antichains. An antichain is a set where any two distinct elemen... |
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.Finite.Defs
import Mathlib.Data.Finset.BooleanAlgebra
import Mathlib.Data.Finset.Image
import Mathlib.Data.Fintype.Defs
import Mathlib.Data.Fintyp... |
PrimeFin.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.Data.Countable.Defs
import Mathlib.Data.Nat.Factors
import Mathlib.Data.Nat.Prime.Infinite
import Mathlib.Data... |
FilteredColimits.lean | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
import Mathlib.CategoryTheory.Limits.Preserves.Filtered
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
import Mathlib.CategoryTheory.Limits.Types.Filter... |
Polynomial.lean | /-
Copyright (c) 2024 Jineon Baek and Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jineon Baek, Seewoo Lee
-/
import Mathlib.Algebra.Polynomial.Expand
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.NumberTheory.FLT.Basic
import Mathlib.NumberThe... |
AbsoluteValue.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Int.AbsoluteValue
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
/-!
# Absolute values and... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
Ring.lean | import Mathlib.Algebra.Category.Ring.Basic
universe v u
open CategoryTheory SemiRingCat
set_option maxHeartbeats 10000
set_option synthInstance.maxHeartbeats 2000
/- We test if all the coercions and `map_add` lemmas trigger correctly. -/
example (X : Type u) [Semiring X] : ⇑(𝟙 (of X)) = id := by simp
example {X ... |
GaussianIntegral.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.Analysis.SpecialFunctions.Gamma.Basic
import Mathlib.Analysis.SpecialFunctions.PolarCoord
import Mathlib.Analysis.Complex.Convex
import Mathlib.D... |
ApproximationCorollaries.lean | /-
Copyright (c) 2021 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Computation.Approximations
import Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv
import Mathlib.Algebra.Order.Archi... |
choice.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.
(**************************************************... |
TuringDegree.lean | /-
Copyright (c) 2025 Tanner Duve. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tanner Duve, Elan Roth
-/
import Mathlib.Computability.Partrec
import Mathlib.Order.Antisymmetrization
/-!
# Oracle Computability and Turing Degrees
This file defines a model of oracle ... |
ExtendToLocalization.lean | /-
Copyright (c) 2022 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.RingTheory.Localization.Defs
import Mathlib.RingTheory.Valuation.Basic
/-!
# Extending valuations to a localization
We show that, given a valuation `v` taki... |
PositiveLinearMap.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.Order.Module.PositiveLinearMap
import Mathlib.Analysis.CStarAlgebra.Classes
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculu... |
Sphere.lean | /-
Copyright (c) 2024 Elliot Dean Young and Jiazhen Xia. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiazhen Xia, Elliot Dean Young
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Topology.Category.TopCat.Basic
/-!
# Euclidean spheres
This files ... |
Pi.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.Eigenspace.Triangularizable
/-!
# Simultaneous eigenvectors and eigenvalues for families of endomorphisms
In finite dimensions, the theory of... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Unique.lean | /-
Copyright (c) 2023 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import Mathlib.Probability.Kernel.Disintegration.Integral
/-!
# Uniqueness of the conditional kernel
We prove that the conditional kernels `ProbabilityTheor... |
Defs.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.NeZero
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Algebra.Ring.GrindInstances
import Mathlib.Da... |
Grp_.lean | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.ExactFunctor
/-!... |
SolutionOfCubicQuartic.lean | /-
Copyright (c) 2022 Jeoff Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeoff Lee, Thomas Zhu
-/
import Mathlib.Tactic.LinearCombination
import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
/-!
# The roots of cubic and quartic polynomials
This file proves Th... |
Defs.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Michael Howes, Antoine Chambert-Loir
-/
import Mathlib.GroupTheory.Commutator.Basic
/-!
# The abelianization of a group
This file defines the commutator and the abelianization ... |
Reindex.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
/-!
# Changing the index type of a matrix
This file concerns the map... |
Algebra.lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Kim Morrison, Yuyang Zhao
-/
import Mathlib.Algebra.Order.ZeroLEOne
import Mathlib.SetTheory.PGame.Order
import Mathlib.Data.Nat.Cast.De... |
RingHom.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Filippo A. E. Nuccio, Andrew Yang
-/
import Mathlib.RingTheory.Spectrum.Prime.Basic
import Mathlib.RingTheory.LocalRing.ResidueField.Ideal
import Mathlib.RingTheory.Ten... |
Energy.lean | /-
Copyright (c) 2022 Yaël Dillies, Ella Yu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Ella Yu
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Fintype.Prod
import Mathlib.Algebra.Group.Poin... |
Products.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.FilteredColimitCommutesProduct
import Mathlib.CategoryTheory.Limits.Indization.FilteredColimits
/-!
# Ind-objects are closed under... |
IsTensorProduct.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.TensorProduct.Basic
/-!
# The characteristic predicate of tensor product
## Main definitions
- `IsTensorProduct`: A predicate on `f : M₁ →ₗ[R] ... |
Field.lean | /-
Copyright (c) 2024 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Analysis.Normed.Group.Continuity
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Defs
/-!
# Infinite sums and produ... |
vcharacter.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... |
HaarToSphere.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Field.Pointwise
import Mathlib.Analysis.NormedSpace.SphereNormEquiv
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Mat... |
Scan.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.Basic
import Mathlib.Order.Basic
import Mathlib.Data.Nat.Basic
impo... |
MeasureSpaceDef.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.MeasureTheory.OuterMeasure.Induced
import Mathlib.MeasureTheory.OuterMeasure.AE
import Mathlib.Order.Filter.CountableInter
/-!
# Measu... |
all.v | From mathcomp Require Export all_boot.
From mathcomp Require Export all_order.
From mathcomp Require Export all_fingroup.
From mathcomp Require Export all_algebra.
From mathcomp Require Export all_solvable.
From mathcomp Require Export all_field.
From mathcomp Require Export all_character.
|
BooleanAlgebra.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Order.CompleteBooleanAlgebra
/-!
# Sets are a complete atomic boolean algebra.
This file contains on... |
commutator.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat fintype.
From mathcomp Require Import bigop finset binomial fingroup morphism.
From mathcomp... |
algnum.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... |
Prod.lean | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Notation.Prod
import Mathlib.Algebra.Regular.SMul
/-!
# Results about `IsRegular` and `Prod`
-/
variable {α R S : Type*}
section
variable [Mul R] ... |
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... |
Abelian.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification
import Mathlib.CategoryTheory.Abelian.Transfer
/-!
# The category of sheaves of modules is abelian
In this f... |
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... |
Basic.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.Algebra.Order.AbsoluteValue.Basic
import Mathlib.Algebra.Ring.Opposite
import Mathlib.Algebra.Ring.Prod
import Mathlib.Algebra.Ring.Sub... |
NCard.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Set.Card
import Mathlib.MeasureTheory.MeasurableSpace.Constructions
/-!
# Measurability of `Set.encard` and `Set.ncard`
In this file we prove ... |
RightHomology.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.LeftHomology
import Mathlib.CategoryTheory.Limits.Opposites
/-!
# Right Homology of short complexes
In this file, we define the ... |
Concept.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.Set.Lattice
/-!
# Formal concept analysis
This file defines concept lattices. A concept of a relation `r : α → β → Prop` is a pair of sets
`s : Set ... |
Images.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.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
/-!
# Preserving images
In this file, we show that if a fu... |
MvPolynomial.lean | /-
Copyright (c) 2023 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
import Mathlib.Algebra.MvPolynomial.Eval
import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Multivariate polynomials and continuity
In this file we prove the... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
HolderNorm.lean | /-
Copyright (c) 2024 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Topology.MetricSpace.Holder
/-!
# Hölder norm
This file defines the Hölder (semi-)norm for Hölder functions alongside some basic properties.
The `r`-Hölder... |
DoubleCoset.lean | /-
Copyright (c) 2021 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Algebra.Group.Subgroup.Pointwise
import Mathlib.GroupTheory.Coset.Basic
/-!
# Double cosets
This file defines double cosets for two subgroups `H K` o... |
Unitization.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.Algebra.Defs
import Mathlib.Algebra.Algebra.NonUnitalHom
import Mathlib.Algebra.Star.Module
import Mathlib.Algebra.Star.NonUnitalSubalgebra
impor... |
IsPowMulFaithful.lean | /-
Copyright (c) 2024 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.AlgebraNorm
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
/-!
# Equivalent power-m... |
preorder.v | (* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import path fintype tup... |
CantorNormalForm.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.SetTheory.Ordinal.Exponential
import Mathlib.SetTheory.Ordinal.Family
/-!
# Cantor Normal Form
The Cantor normal form of an ordinal is generally defi... |
extremal.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 bigo... |
Json.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.Init
/-!
# Json serialization typeclass for `PUnit` & `Fin n` & `Subtype p`
-/
universe u
namespace Lean
deriving instance FromJson, ToJson for PUnit
... |
Symmetric.lean | import Mathlib.Algebra.Category.AlgCat.Monoidal
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric
deprecated_module (since := "2025-05-11")
|
Defs.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Algebra.Subalgebra.Lattice
/-!
# Central Algebras
In this file we define the predicate `Algebra.IsCentral K D` where `K` is a commutative ring a... |
Localization.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.HomotopyCofiber
import Mathlib.Algebra.Homology.HomotopyCategory
import Mathlib.Algebra.Homology.QuasiIso
import Mathlib.CategoryTheory.Localiz... |
ActionHom.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.GroupTheory.GroupAction.DomAct.Basic
import Mathlib.GroupTheory.GroupAction.Hom
/-!
# Action of `Mᵈᵐᵃ` on `α →[N] β` and `A →+[N] B`
In this file we... |
NoAtoms.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.MeasureTheory.Measure.Restrict
/-!
# Measures having no atoms
A measure `μ` has no atoms if the measure of each singleton is zero.
#... |
NeZero.lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Logic.Basic
import Mathlib.Order.Defs.PartialOrder
/-!
# `NeZero` typeclass
We give basic facts about the `NeZero n` typeclass.
-/
variable {R : Ty... |
DiffContOnCl.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.NormedSpace.Real
import Mathlib.Analysis.Calculus.FDeriv.Add
import Mathlib.Analysis.Calculus.FDeriv.Mul
/-!
# Functions differentiable on ... |
PrimitiveRoots.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Data.Nat.Factorization.LCM
import Mathlib.Algebra.Group.TypeTags.Finite
import Mathlib.RingTheory.RootsOfUnity.Basic
/-!
# Primitive roots of unity
We... |
Central.lean | /-
Copyright (c) 2021 Patrick Stevens. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Stevens, Thomas Browning
-/
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Nat.GCD.Basic
import Mathlib.Tactic.Ring
import Mathlib.Tactic.Linarith
/-!
# Central bin... |
Basic.lean | /-
Copyright (c) 2019 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Module.Submodule.Equiv
import Mathlib.Algebra.Module.Equiv.Basic
import Mathlib.Algebra.Module.Rat
import Mathlib.Data.Bracket
import Mathlib.Tactic.... |
Lipschitz.lean | /-
Copyright (c) 2018 Rohan Mitta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rohan Mitta, Kevin Buzzard, Alistair Tucker, Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.ProjIcc
import Mathlib.Topology.Bornology.Hom
import Mathlib.Topology.EMe... |
Approximations.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Determinant
import Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating
import Mathlib.Algebra.Order.Ri... |
Lemmas.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Yury Kudryashov
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.List.InsertIdx
/-! # Some lemmas about lists involving sets
Split out from `Data.List.Basic` to... |
Bifunctor.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier, Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Fubini
import Mathlib.CategoryTheory.Functor.Currying
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.Cate... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
Lemmas.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Init
/-! Lemmas use by the congruence closure module -/
namespace Mathlib.Tactic.CC
theorem iff_eq_of_eq_true_left {a b : Prop} (h : a = ... |
DecisionSuf.lean | /-
Copyright (c) 2020 Gihan Marasingha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gihan Marasingha
-/
import Archive.MiuLanguage.DecisionNec
import Mathlib.Tactic.Linarith
/-!
# Decision procedure - sufficient condition and decidability
We give a sufficient cond... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
finset.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat div seq.
From mathcomp Require Import choice fintype finf... |
Stalks.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.Geometry.RingedSpace.PresheafedSpace
import Mathlib.CategoryTheory.Limits.Final
import Mathlib.Topology.Sheaves.Stalks
/-!
# Stalks for presheaved spaces
... |
all_field.v | From mathcomp Require Export algC.
From mathcomp Require Export algebraics_fundamentals.
From mathcomp Require Export algnum.
From mathcomp Require Export closed_field.
From mathcomp Require Export cyclotomic.
From mathcomp Require Export falgebra.
From mathcomp Require Export fieldext.
From mathcomp Require Export fin... |
BddLat.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.CategoryTheory.Adjunction.Unique
import Mathlib.Order.Category.BddOrd
import Mathlib.Order.Category.Lat
import Mathlib.Order.Category.Semilat
import Mathli... |
Name.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Init
import Lean.Meta.Match.MatcherInfo
import Lean.Meta.Tactic.Delta
import Std.Data.HashMap.Basic
/-!
# Additional functions on `Lean.Name`.
We provide... |
FunLike.lean | import Mathlib.Data.FunLike.Basic
variable {F α β : Sort*} [i : FunLike F α β] (f : F) (a : α)
/-- info: f a : β -/
#guard_msgs in #check f a
|
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.
(**********************... |
Exposed.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Extreme
import Mathlib.Analysis.Convex.Function
import Mathlib.Topology.Algebra.Module.LinearMap
import Mathlib... |
Lemmas.lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Batteries.Tactic.Lint.Basic
import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Order.ZeroLEOne... |
Closed.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Kim Morrison, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.CategoryTheory.Linear.Yoneda
import Mathlib.Algebra.Category.ModuleCat.Monoi... |
prime.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div bigop.
(*************************... |
KaroubiKaroubi.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.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotence of the Karoubi envelope
In this file, we construct the equivalence of categories
`KaroubiKaroubi.equivalen... |
Basic.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.Basic
/-!
# Multivariate quotients of polynomial functors.
Basic definition of multivariate QPF. QPFs form a co... |
Posterior.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Probability.Kernel.CompProdEqIff
import Mathlib.Probability.Kernel.Composition.Lemmas
import Mathlib.Probability.Kernel.Disintegration.StandardBorel
/-!
... |
sesquilinear.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup.
From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector.
(************************************************... |
IntegrallyClosed.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.RingTheory.IntegralClosure.IntegrallyClosed
import Mathlib.RingTheory.Valuation.ValuationRing
/-!
# Valuation subring is integrally closed
-/
name... |
Linear.lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Linear
/-!
# Derivatives of continuous linear maps from the base ... |
Basic.lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Normed.Operator.LinearIsometry
import Mathlib.Algebra.S... |
Floor.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Algebra.Order.Floor.Ring
import Mathlib.Order.Filter.AtTopBot.Floor
import Mathlib.Topology.Algebra.Order.Group
/-!
# Topological facts about `Int... |
ModuleCat.lean | import Mathlib.Algebra.Category.ModuleCat.Basic
universe v u
open CategoryTheory ModuleCat
set_option maxHeartbeats 10000
set_option synthInstance.maxHeartbeats 2000
variable (R : Type u) [CommRing R]
/- We test if all the coercions and `map_add` lemmas trigger correctly. -/
example (X : Type v) [AddCommGroup X] ... |
Prod.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Patrick Massot
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.SProd
/-!
# Sets in product and pi types
This file proves basic properties of prod... |
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... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
Operations.lean | /-
Copyright (c) 2023 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Combinatorics.SimpleGraph.Finite
import Mathlib.Combinatorics.SimpleGraph.Maps
import Mathlib.Combinatorics.SimpleGraph.Subgraph
/-!
# Local graph operations
... |
Constructions.lean | /-
Copyright (c) 2021 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Topology.Separation.Hausdorff
import Mathlib.Topology.Homeomorph.Lemmas
/-!
# Topological space structure on the opposite monoid and on the units ... |
MapComap.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Probability.Kernel.Basic
/-!
# Map of a kernel by a measurable function
We define the map and comap of a kernel along a measurable func... |
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