filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Limits.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.Topology.Category.CompHausLike.Limits
import Mathlib.Topology.Category.Stonean.Basic
/-!
# Explicit l... |
Basic.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Jujian Zhang
-/
import Mathlib.Algebra.Algebra.Tower
import Mathlib.Algebra.Module.TransferInstance
import Mathlib.RingTheory.Localization.Defs
/-!
# Localized Module
Give... |
Functor.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Closed.Cartesian
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Adjunction.FullyFaithful... |
RegularSheaves.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.Limits.Final.ParallelPair
import Mathlib... |
MulOpposite.lean | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.FiniteDimensional.Defs
/-!
# Basis of an opposite space
This file defines the basis of an opposite space and shows
that the opposite space is... |
Prod.lean | /-
Copyright (c) 2022 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Yury Kudryashov, Kevin H. Wilson, Heather Macbeth
-/
import Mathlib.Order.Filter.Tendsto
/-!
# Product and coproduct filters
In this file we define `F... |
ssrnotations.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
(******************************************************************************)
(* - Reserved notation for various arithmetic and algebraic operations: ... |
Hermitian.lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.LinearAlgebra.Matrix.ZPow
import Mathlib.Data.Matrix.ConjTranspose
/-! # Hermitian matrices
Th... |
FactorThru.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Kim Morrison
-/
import Mathlib.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.Preadditive.Basic
/-!
# Factoring through subobjects
The predicate `h : P.Fact... |
Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Centers of rings
-/
assert_not_exists RelIso Finset Subsemigroup Field
vari... |
LebesgueNormedSpace.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.MeasureTheory.Measure.WithDensity
import Mathlib.Analysis.Normed.Module.Basic
/-! # A lemma about measurability with density under scalar multip... |
countalg.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ss... |
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.... |
perm.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype tup... |
MeanInequalities.lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Analysis.MeanInequalities
import Mathlib.Analysis.MeanInequalitiesPow
import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic
import Mathlib.MeasureTh... |
ADEInequality.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Data.Multiset.Sort
import Mathlib.Data.PNat.Basic
import Mathlib.Data.PNat.Interval
import Mathlib.Tactic.NormNum... |
TotallyDisconnected.lean | /-
Copyright (c) 2024 Jou Glasheen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jou Glasheen, Kevin Buzzard, David Loeffler, Yongle Hu, Johan Commelin
-/
import Mathlib.Topology.Algebra.Nonarchimedean.Basic
/-!
# Total separatedness of nonarchimedean groups
In th... |
Basic.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.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric
import Mathlib.Analysis.CStarAlgebra.GelfandDuality
import Mathlib.Analysis.CStarAlgebra.Uni... |
Bilinear.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.Algebra.Algebra.NonUnitalHom
import Mathlib.LinearAlgebra.TensorProduct.Basic
/-!
# Facts about algebras involving bilinear maps and tensor pro... |
Triangulated.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.HomotopyCategory.Pretriangulated
import Mathlib.CategoryTheory.Triangulated.Triangulated
import Mathlib.CategoryTheory.ComposableArrows
/-! The... |
Inductions.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Damiano Testa, Jens Wagemaker
-/
import Mathlib.Algebra.MonoidAlgebra.Division
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mat... |
Canonical.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin, Patrick Massot
-/
import Mathlib.Algebra.GroupWithZero.InjSurj
import Mathlib.Algebra.GroupWithZero.WithZero
import Mathlib.Algebra.Order.AddGroupWithTop
import M... |
Partial.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Order.Filter.Tendsto
import Mathlib.Data.PFun
/-!
# `Tendsto` for relations and partial functions
This file generalizes `Filter` definitions from funct... |
numfield.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... |
PPWithUniv.lean | /-
Copyright (c) 2023 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Mathlib.Init
/-!
# Attribute to pretty-print universe level parameters by default
This module contains the `pp_with_univ` attribute, which enables pret... |
StructuredArrow.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.Localization.HomEquiv
import Mathlib.CategoryTheory.Localization.Opposite
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
/-!
# Inducti... |
MapDomain.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, Kim Morrison
-/
import Mathlib.Algebra.MonoidAlgebra.Defs
import Mathlib.Data.Finsupp.SMul
/-!
# MonoidAlgebra.mapDomain
-/
assert_not_exists NonUni... |
Arithmetic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Data.Nat.SuccPred
import Mathlib.Order.IsNormal
import ... |
DirectedInverseSystem.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Order.SuccPred.Limit
import Mathlib.Order.UpperLower.Basic
/-!
# Definition of direct systems, inverse systems, and cardinalities in specific inverse systems
T... |
galois.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
Orthogonal.lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import Mathlib.Data.Matrix.Mul
/-!
# Orthogonal
This file contains definitions and properties concerning orthogonality of rows and columns.
## Main results
- `matri... |
inertia.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div... |
LexOrder.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.RingTheory.MvPowerSeries.Basic
import Mathlib.Data.Finsupp.WellFounded
/-! LexOrder of multivariate power series
Given an ordering of ... |
measurability.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.MeasureTheory.MeasurableSpace.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.MeasureTheory.Function.SpecialFunctions.Basi... |
Bounds.lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.SpecificFunctions.Deriv
import Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
/-!
# Polynomia... |
Polynomial.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Eric Wieser
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Analysis.Calculus.Deriv.Mul
import Mathlib... |
Even.lean | /-
Copyright (c) 2024 Artie Khovanov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Artie Khovanov
-/
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.Group.Subgroup.Defs
/-!
# Squares and even elements
This file defines the subgroup of squares / even elemen... |
Basic.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather, Yury Kudryashov
-/
import Mathlib.CategoryTheory.Types
/-!
# Concrete categories
A concrete category is a category `C` where th... |
PPRoundtrip.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Lean.Elab.Command
import Mathlib.Init
/-!
# The "ppRoundtrip" linter
The "ppRoundtrip" linter emits a warning when the syntax of a command differs substantia... |
Zorn.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Order.CompleteLattice.Chain
import Mathlib.Order.Minimal
/-!
# Zorn's lemmas
This file proves several formulations of Zorn's Lemma.
## Variants
The... |
CountablyGenerated.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, Patrick Massot
-/
import Mathlib.Data.Set.Countable
import Mathlib.Order.Filter.Bases.Finite
/-!
# Countably generated filters
In this file we define a... |
Nth.lean | /-
Copyright (c) 2024 Ralf Stephan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ralf Stephan
-/
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Nat.Nth
/-!
# The Nth primes
-/
namespace Nat
@[simp]
theorem nth_prime_zero_eq_two : nth Prime 0 = 2 := nth_cou... |
Simp.lean | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
import Lean.Meta.Tactic.Simp.Types
import Mathlib.Init
import Qq
/-! # Additional simp utilities
This file adds additional tools for metaprogramming with the `simp` tacti... |
MeasurePreserving.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.AEMeasurable
import Mathlib.Order.Filter.EventuallyConst
/-!
# Measure preserving maps
We say that `f : α → β` is a measure p... |
Cyclic.lean | /-
Copyright (c) 2025 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.Algebra.Order.Group.Basic
import Mathlib.GroupTheory.SpecificGroups.Cyclic
... |
Equiv.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.Algebra.AddConstMap.Basic
/-!
# Equivalences conjugating `(· + a)` to `(· + b)`
In this file we define `AddConstEquiv G H a b` (notation: `G ≃+c[a,... |
Basic.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.Exact
import Mathlib.LinearAlgebra.Span.Basic
import Mathlib.RingTheory.Ideal.IsPrimary
import Mathlib.RingTheory.Ideal.Quotient.Operations
import Ma... |
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, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Submonoid.Basic
import Mathlib.Algebra.Ring... |
polydiv.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 choice.
From mathcomp Require Import fintype bigop ssralg poly.
(**********************... |
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... |
order.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... |
Exp.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Analysis.Complex.Periodic
import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
/-!
# Exp ... |
mxred.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 div.
From mathcomp Require Import choice fintype finfun bigop fingroup perm order.
From ... |
Polynomial.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.MvPolynomial.Equiv
/-!
# Some lemmas relating polynomials and multivariable polynomials.
-/
namespace MvPolynomial
variable {R S σ : Type*}
the... |
SimplicialObject.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.AlgebraicTopology.SimplicialCategory.Basic
import Mathlib.CategoryTheory.Functor.FunctorHom
/-!
# The category of simplicial objects is simplicial
In `Category... |
Basic.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot, Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
import Math... |
Synonym.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.RingTheory.Finiteness.Defs
import Mathlib.Topology.Bornology.Constructions
import Mathlib.Topology.UniformSpace.Equiv
import Mathlib.Topology.Algebra.Mod... |
Units.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.Analysis.Normed.Ring.Units
import Mathlib.Algebra.Algebra.Spectrum.Basic
import Mathlib.Topology.ContinuousMap.Algebra
/-!
# Units of continuous functio... |
countalg.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ss... |
JapaneseBracket.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.SpecialFunctions.Integrability.Basic
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.Integral.Layercake
/-!
# Jap... |
Basic.lean | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Analysis.Convex.Hull
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Topology.Bornology.A... |
ChangeOfRings.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.Algebra.Category.ModuleCat.EpiMono
import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Algeb... |
Image.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Yaël Dillies
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Data.Set.Function
import Mathlib.Order.Directed
/-!
# Monotone functions on intervals
This file sho... |
zmodp.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool choice eqtype ssrnat seq.
From mathcomp Require Import div fintype bigo... |
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... |
Upcrossing.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.Order.Interval.Set.Monotone
import Mathlib.Probability.Process.HittingTime
import Mathlib.Probability.Martingale.Basic
import Mathlib.Tactic.AdaptationNote
... |
alt.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 tupl... |
Stalk.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Fangming Li
-/
import Mathlib.AlgebraicGeometry.AffineScheme
import Mathlib.AlgebraicGeometry.Morphisms.Preimmersion
/-!
# Stalks of a Scheme
## Main definitions and result... |
Canonical.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Order.Sub.Basic
impo... |
Basic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Bhavik Mehta, Stuart Presnell
-/
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Order.Monotone.Defs
/-!
# Binomial coefficients
This file defines binomial coeffic... |
bigop.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
Yoneda.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.Algebra.Category.Grp.Abelian
import Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four
import Mathlib.CategoryTheory.Abelian.Projective.Basic
import Mathl... |
ToSquareZero.lean | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-/
import Mathlib.RingTheory.Derivation.Basic
import Mathlib.RingTheory.Ideal.Quotient.Operations
/-!
# Results
- `derivationToSquareZeroOfLift`: The ... |
M.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import Mathlib.Data.PFunctor.Multivariate.Basic
import Mathlib.Data.PFunctor.Univariate.M
/-!
# The M construction as a multivariate polyn... |
Cokernel.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Module.Presentation.Basic
/-!
# Presentation of a cokernel
If `f : M₁ →ₗ[A] M₂` is a linear map between modules,
`pres₂` is a presentation of `M₂` and ... |
Basic.lean | import Mathlib.Tactic.RewriteSearch
set_option autoImplicit true
-- You can enable tracing of the `rw_search` algorithm using
-- set_option trace.rw_search true
-- You can get timing information (very useful if tweaking the search algorithm!) using
-- set_option profiler true
/--
info: Try this: rw [List.length_ap... |
Flatten.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn, Mario Carneiro, Martin Dvorak
-/
import Mathlib.Tactic.GCongr.Core
import Mathlib.Util.AssertExists
/-!
# Join of a list of lists
This file prove... |
levenshtein.lean | import Mathlib.Data.List.EditDistance.Defs
import Mathlib.Algebra.Group.Nat.Defs
#guard
(suffixLevenshtein Levenshtein.defaultCost "kitten".toList "sitting".toList).1 =
[3, 3, 4, 5, 6, 6, 7]
#guard levenshtein Levenshtein.defaultCost
"but our fish said, 'no! no!'".toList
"'put me down!' said the fish.".toLi... |
Finite.lean | /-
Copyright (c) 2025 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.RingTheory.Finiteness.Basic
/-!
# A finite direct sum of finite modules is finite
This file defines a `Module.Fin... |
Orthonormal.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.InnerProductSpace.LinearMap
import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
import Mathlib.RingTheory... |
finfield.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype div tupl... |
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... |
Factorization.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.Basic
/-!
# The factorization axiom
In this file, we introduce a type-class `HasFactorization W₁ W₂`, which, given
two classes ... |
FourierMotzkin.lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Std.Data.HashMap
import Batteries.Lean.HashMap
import Mathlib.Tactic.Linarith.Datatypes
/-!
# The Fourier-Motzkin elimination procedure
The Fourier... |
field.lean | import Mathlib
example (x y : ℝ) (h : x ≠ y) : (x^2 - y^2)/(x - y) = x + y := by grind
example (x y : ℝ) (h : (x + y)^2 ≠ 0) : (x^2 - y^2)/(x + y) = x - y := by grind
|
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, Yury Kudryashov
-/
import Mathlib.Algebra.Module.LinearMap.Defs
/-!
# Algebras over commutative semirings
In this file we define associative unital `Algebra`s over commutative ... |
Asymptotics.lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic
import Mathlib.Analysis.Asymptotics.Defs
/-!
# Asymptotic statements about th... |
OrderIso.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.Order.Bounds.Image
import Mathlib.Order.Hom.Set
/-!
# Order isomorphisms and bounds.
-/
open Set
namespace OrderIso
variable {α β ... |
Parity.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Nat.Even
import Mathlib.Data.Nat.Cast.Basic
import Mathlib.Data.Nat.Cast.Commute
import Mathlib.Data.Set.Operations
import Mathlib.Logic.Fu... |
Ideal.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Wojciech Nawrocki
-/
import Mathlib.Data.Matrix.Basis
import Mathlib.GroupTheory.Congruence.BigOperators
import Mathlib.RingTheory.Ideal.Lattice
import Mathlib.RingTheory.T... |
Paracompact.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Yury Kudryashov
-/
import Mathlib.Data.Option.Basic
import Mathlib.Topology.Separation.Regular
/-!
# Paracompact topological spaces
A topological space `X` is said to b... |
AbelRuffini.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Analysis.Calculus.LocalExtr.Polynomial
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.FieldTheory.AbelRuffini
import Mathlib.RingThe... |
finmodule.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... |
Matrix.lean | /-
Copyright (c) 2025 Bryan Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Wang
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.Diagonal
import Mathlib.Algebra.Algebra.Subalgebra.Basic
/-!
# Matrix subalgebras
In this file we define the sub... |
Kernels.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin, Kim Morrison
-/
import Mathlib.Analysis.Normed.Group.SemiNormedGrp
import Mathlib.Analysis.Normed.Group.Quotient
import Mathlib.CategoryTheory.Limits.Sha... |
ConstMulAction.lean | /-
Copyright (c) 2021 Alex Kontorovich, Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth
-/
import Mathlib.Algebra.Group.Pointwise.Set.Lattice
import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set
import Mathlib.Alge... |
StronglyRegular.lean | /-
Copyright (c) 2021 Alena Gusakov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Jeremy Tan
-/
import Mathlib.Combinatorics.Enumerative.DoubleCounting
import Mathlib.Combinatorics.SimpleGraph.AdjMatrix
/-!
# Strongly regular graphs
## Main definitio... |
TopCommRingCat.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.Algebra.Category.Ring.Basic
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Algebra.Ring.Basic
/-!
# Category of topological commuta... |
sylow.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 prime bigop finset fingroup morphism.
From mat... |
Basic.lean | /-
Copyright (c) 2025 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Anne Baanen
-/
import Mathlib.Algebra.Polynomial.Degree.Definitions
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
/-!
# Resultant of two polynomials
This file contains... |
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