filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
NonUnitalSubalgebra.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.NonUnitalHom
import Mathlib.Data.Set.UnionLift
import Mathlib.LinearAlgebra.Span.Basic
import Mathlib.RingTheory.NonUnitalSubring.Basic
... |
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.... |
Isocrystal.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.RingTheory.WittVector.FrobeniusFractionField
/-!
## F-isocrystals over a perfect field
When `k` is an integral domain, so is `𝕎 k`, and we can co... |
TangentCone.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Convex.Topology
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Seminorm
import Mathlib.Analysis.SpecificLimits.Basi... |
basicTactics.lean | import Mathlib.Tactic.Basic
import Batteries.Tactic.Init
example : ∀ a b : Nat, a = b → b = a := by
introv h
exact h.symm
set_option linter.unusedTactic false in
example (n : Nat) : n = n := by
induction n
exacts [rfl, rfl]
exacts []
set_option linter.unusedVariables false in
example (n : Nat) : Nat := by
... |
Contractible.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Topology.Homotopy.Path
import Mathlib.Topology.Homotopy.Equiv
/-!
# Contractible spaces
In this file, we define `ContractibleSpace`, a space ... |
Order.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, Kexing Ying
-/
import Mathlib.Topology.Semicontinuous
import Mathlib.MeasureTheory.Function.AEMeasurableSequence
import Mathlib.MeasureTheory.Order.Lat... |
Module.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu, Anne Baanen
-/
import Mathlib.Algebra.Module.LocalizedModule.IsLocalization
import Mathlib.LinearAlgebra.Basis.Basic
import Mathlib.RingTheory.Localization.FractionRing
import ... |
Module.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.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCat.FilteredColimits
im... |
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... |
Semiprimary.lean | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.RingTheory.Jacobson.Radical
import Mathlib.RingTheory.Nilpotent.Defs
import Mathlib.RingTheory.SimpleModule.Basic
/-!
# Semiprimary rings
## Main definition
*... |
Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.RingTheory.Ideal.Over
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
import Mathlib.RingT... |
fintype.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 ssrnotations eqtype.
From mathcomp Require Import ssrnat seq choice pat... |
AList.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.Data.Finsupp.Basic
import Mathlib.Data.List.AList
/-!
# Connections between `Finsupp` and `AList`
## Main definitions
* `Fin... |
Range.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir and Filippo Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.Algebra.Group.Subgroup.Pointwise
import Mathlib.Algebra.GroupWi... |
Bipointed.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.Category.Pointed
/-!
# The category of bipointed types
This defines `Bipointed`, the category of bipointed types.
## TODO
Monoidal struc... |
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
-/
import Mathlib.Algebra.Notation.Support
import Mathlib.Topology.Inseparable
import Mathlib.Topology.Piecewise
import Mathlib.Topology.Separation.Separ... |
InjSurj.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, Johannes Hölzl
-/
import Mathlib.Algebra.Order.Monoid.Basic
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module (since := ... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Multiset.lean | /-
Copyright (c) 2021 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.BigOperators.Group.Multiset.Defs
import Mathlib.Algebra.Order.BigOperators.Ring.List
/-!
# Big operators on a multiset in ordered ring... |
Sqrt.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Data.Nat.Sqrt
import Mathlib.Tactic.Common
/-!
# Square root of integers
This file defines the square root function on integers. `Int.sqrt z` is the greatest i... |
Braided.lean | /-
Copyright (c) 2024 Gareth Ma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gareth Ma
-/
import Mathlib.CategoryTheory.Monoidal.Rigid.Basic
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
/-!
# Deriving `RigidCategory` instance for braided and left/right rigi... |
Derivative.lean | /-
Copyright (c) 2023 Richard M. Hill. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Richard M. Hill
-/
import Mathlib.RingTheory.PowerSeries.Trunc
import Mathlib.RingTheory.PowerSeries.Inverse
import Mathlib.RingTheory.Derivation.Basic
/-!
# Definitions
In this fil... |
Chain.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.Data.Set.Lattice
import Mathlib.Order.Preorder.Chain
/-!
# Hausdorff's maximality principle
This file proves Hausdorff's maximality principle.
## Ma... |
Subring.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.CharP.Algebra
/-!
# Characteristic of subrings
-/
universe u v
namespace CharP
instance subsemiring (R : Type u) [Semiring R] (p : ℕ) [CharP R p] (S... |
Idempotent.lean | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Ring.Idempotent
import Mathlib.Order.BooleanAlgebra.Defs
import Mathlib.Order.Hom.Basic
/-!
# Boolean algebra structure on idempotents in a commutative ... |
Dvd.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Patrick Stevens
-/
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Nat.Prime.Factorial
/-!
# Divisibility properties of binomial coefficients
-/
namespace Nat
... |
Adjoint.lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Adjoint of operators on Hilbert spaces
Given ... |
Finset.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies, Andrew Yang
-/
import Mathlib.Algebra.Order.GroupWithZero.Canonical
import Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso
import Mathlib.Data.Finset.Lat... |
Projective.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.Topology.Category.Profinite.Basic
import Mathlib.Topology.Compactification.StoneCech
import Mathlib.CategoryTheory.Preadditive.Projective.Basic
import ... |
archimedean.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 or... |
TensorProduct.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Andrew Yang
-/
import Mathlib.RingTheory.HopfAlgebra.Basic
import Mathlib.RingTheory.Bialgebra.TensorProduct
/-!
# Tensor products of Hopf algebras
We define th... |
Degenerate.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.SimplicialSet.Basic
/-!
# Degenerate simplices
Given a simplicial set `X` and `n : ℕ`, we define the sets `X.degenerate n`
and `X.nonDegenera... |
Truncated.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.RingTheory.WittVector.InitTail
/-!
# Truncated Witt vectors
The ring of truncated Witt vectors (of length `n`) is a quotient of the... |
Multiplicity.lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Chris Hughes, Daniel Weber
-/
import Batteries.Data.Nat.Gcd
import Mathlib.Algebra.GroupWithZero.Associated
import Mathlib.Algebra.Ring.Divisibility.Basic
import Math... |
Preprocessing.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.Tactic.Linarith.Datatypes
import Mathlib.Tactic.Zify
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.Control.Basic
import Mathlib.Util.AtomM
... |
SplitCoequalizer.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.Limits.Shapes.Equalizers
/-!
# Split coequalizers
We define what it means for a triple of morphisms `f g : X ⟶ Y`, `π : Y ⟶ Z` to be a spl... |
all_algebra.v | (* N.B. interval_inference is not exported here.
To enjoys the automation it provides,
you need to explictly "Import interval_inference". *)
From mathcomp Require Export ssralg.
From mathcomp Require Export ssrnum.
From mathcomp Require Export finalg.
From mathcomp Require Export countalg.
From mathcomp Require Export... |
Basis.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-/
import Mathlib.LinearAlgebra.Basis.Defs
import Mathlib.LinearAlgebra.Dual.Defs
/-!
# Bases of dual vector spaces
The dual space of an $... |
Card.lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.SetTheory.Cardinal.Finite
/-!
# Cardinality of finite types
The cardinality of a finite type `α` is given by `Nat.card α`. This function has
the "junk val... |
Dual.lean | /-
Copyright (c) 2023 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.IndepAxioms
/-!
# Matroid Duality
For a matroid `M` on ground set `E`, the collection of complements of the bases of `M` is the
collection o... |
KonigLemma.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Fintype.Pigeonhole
import Mathlib.Order.Atoms.Finite
import Mathlib.Order.Grade
import Mathlib.Tactic.ApplyFun
/-!
# Kőnig's infinity lemma
Kőnig's ... |
FundThmCalculus.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.Analysis.Calculus.Deriv.Add
import Mathlib.Analysis.Calculus.Deriv.Comp
import Mathlib.Analysis.Calculus.FDeriv.Me... |
Yoneda.lean | /-
Copyright (c) 2025 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
import Mathlib.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.CategoryTheory.Yoneda
/-!
# Yoneda embedding... |
Defs.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Batteries.Data.Rat.Lemmas
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Rat.Init
import Mathlib.Order.Basic
import Mathlib.Tactic.Commo... |
Cartan.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.CartanSubalgebra
import Mathlib.Algebra.Lie.Weights.Basic
/-!
# Weights and roots of Lie modules and Lie algebras with respect to Cartan subalge... |
ULift.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.CategoryTheory.Equivalence
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Data.ULift
/-!
# Basic API for UL... |
CountableDenseLinearOrder.lean | /-
Copyright (c) 2020 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Order.Ideal
import Mathlib.Data.Finset.Max
/-!
# The back and forth method and countable dense linear orders
## Results
Suppose `α β` are linear orders, wit... |
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, Sophie Morel, Yury Kudryashov
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Logic.Embedding.Basic
import Mathlib.Data.Fintype.Car... |
Pairwise.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 Batteries.Data.List.Pairwise
import Mathlib.Logic.Pairwise
import Mathlib.Logic.Relation
/-!
# Pairwise relations on a list
This file provides basic results ... |
spectral.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp.
From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector.
From mathcomp Require Import mxpoly mxred sesqui... |
Hausdorff.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.Analysis.Convex.Between
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
import Mathli... |
NeZero.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.NeZero
/-!
# `NeZero 1` in a nontrivial `MulZeroOneClass`.
This file exists to minimize the depende... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Sqrt.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.Analysis.Calculus.ContDiff.Operations
import Mathlib.Analysis.Calculus.Deriv.Pow
/-!
# Smoothness of `Real.sqrt`
In this file we prove that `Real.s... |
ExactFunctor.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.Homology.DerivedCategory.Basic
/-!
# An exact functor induces a functor on derived categories
In this file, we show that if `F : C₁ ⥤ C₂` is an exact f... |
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... |
path.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.
(******************************************************************************)
(* ... |
PowerBasis.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.FieldTheory.Minpoly.Field
import Mathlib.LinearAlgebra.SModEq
import Mathlib.RingTheory.Ideal.BigOperators
/-!
# Power basis
This file defines a structure ... |
Defs.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.Set.Countable
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Tactic.FunProp.Attr
import Mathlib.Tactic.Mea... |
Projective.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.Topology.Category.CompHaus.Basic
import Mathlib.Topology.Compactification.StoneCech
import Mathlib.CategoryTheory.Preadditive.Projective.Basic
import M... |
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... |
Field.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Patrick Stevens
-/
import Mathlib.Algebra.Order.Field.Basic
/-!
# Cast of naturals into ordered fields
This file concerns the canonical homomorphism `ℕ ... |
IsSepClosed.lean | /-
Copyright (c) 2023 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.FieldTheory.Galois.Basic
/-!
# Separably Closed Field
In this file we define the typeclass for separably closed fields and separable closures,
and prove some of thei... |
Adapted.lean | /-
Copyright (c) 2021 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.Process.Filtration
import Mathlib.Topology.Instances.Discrete
/-!
# Adapted and progressively measurable processes
This file defi... |
all_character.v | From mathcomp Require Export character.
From mathcomp Require Export classfun.
From mathcomp Require Export inertia.
From mathcomp Require Export integral_char.
From mathcomp Require Export mxabelem.
From mathcomp Require Export mxrepresentation.
From mathcomp Require Export vcharacter.
|
GradedMulAction.lean | /-
Copyright (c) 2022 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Eric Wieser
-/
import Mathlib.Algebra.GradedMonoid
/-!
# Additively-graded multiplicative action structures
This module provides a set of heterogeneous typeclasses for de... |
IsBoundedAtImInfty.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.Complex.UpperHalfPlane.FunctionsBoundedAtInfty
import Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs
import Mathlib.NumberTheory.Mod... |
Pi.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Pi.Basic
/-!
# Pi instances for groups with zero
This file de... |
Filter.lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import Mathlib.Order.Filter.EventuallyConst
import Mathlib.RingTheory.Noetherian.Defs
/-!
# Noetherian modules and finiteness of chains... |
List.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
import Mathlib.Algebra.BigOperators.Group.List.Basic
/-!... |
mxabelem.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... |
Unitization.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Unitization
import Mathlib.Algebra.Star.Subalgebra
import Mathlib.GroupTheory.GroupAction.Ring
/-!
# Relating unital and non-unital subs... |
Pointwise.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.End
import Mathlib.Algebra.Group.Pointwise.Set.Lattice
import Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas
import Mathlib.Algebra.Gr... |
Order.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
deprecated_module (since := "2025-04-13")
|
IsSheafFor.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.Sites.Sieves
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
/-!
# The sheaf condition for a presieve
We define what it means fo... |
Engel.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Nilpotent
import Mathlib.Algebra.Lie.Normalizer
/-!
# Engel's theorem
This file contains a proof of Engel's theorem providing necessary and suf... |
Sequential.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.CategoryTheory.Elementwise
import Mathlib.Topology.Sequences
import Mathlib.Topology.Instances.Discrete
import Mathlib.Topology.Category.TopCat.Bas... |
RingHomProperties.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.AlgebraicGeometry.Morphisms.Constructors
import Mathlib.RingTheory.LocalProperties.Basic
import Mathlib.RingTheory.RingHom.Locally
/-!
# Properties of morp... |
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... |
MulOpposite.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.Algebra.Subalgebra.Lattice
import Mathlib.Algebra.Ring.Subring.MulOpposite
/-!
# Subalgebras of opposite rings
For every ring `A` over a commutative ring `R... |
Totient.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.CharP.Two
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Data.Nat.Cast.Field
import Mathlib.Data.Nat.Factorization.Basic
impo... |
Card.lean | /-
Copyright (c) 2024 Thomas Lanard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, Inna Capdeboscq, Johan Commelin, Thomas Lanard, Peiran Wu
-/
import Mathlib.Data.Matrix.Rank
import Mathlib.FieldTheory.Finiteness
import Mathlib.LinearAlgebra.Matrix.Ge... |
Basic.lean | /-
Copyright (c) 2023 Ali Ramsey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ali Ramsey, Eric Wieser
-/
import Mathlib.LinearAlgebra.TensorProduct.Finiteness
import Mathlib.LinearAlgebra.TensorProduct.Associator
/-!
# Coalgebras
In this file we define `Coalgebra`... |
Circular.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.Lattice
import Mathlib.Tactic.Order
/-!
# Circular order hierarchy
This file defines circular preorders, circular partial orders and circular order... |
Basic.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Homology.ConcreteCategory
import Mathlib.RepresentationTheory.Coinvariants
import Mathlib.RepresentationTheory.Homological.Resolution
imp... |
ToBatteries.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Init
/-!
## `funProp` missing function from standard library
-/
namespace Mathlib
open Lean Meta
namespace Meta.FunProp
/-- Check if `a` can be obtai... |
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, Sébastien Gouëzel, Heather Macbeth
-/
import Mathlib.Analysis.Convex.Slope
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.LinearCombination
... |
LongExactSequence.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Homology.ConcreteCategory
import Mathlib.Algebra.Homology.HomologicalComplexAbelian
import Mathlib.RepresentationTheory.Homological.Group... |
push_neg.lean | /-
Copyright (c) 2022 Alice Laroche. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alice Laroche, Frédéric Dupuis, Jireh Loreaux
-/
import Mathlib.Order.Defs.LinearOrder
import Mathlib.Tactic.Push
private axiom test_sorry : ∀ {α}, α
set_option autoImplicit true
vari... |
WellPowered.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.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Well-powered categories
A category `(C : Type u) [Category.{v} C]` is... |
Divisors.lean | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Bhavik Mehta
-/
import Mathlib.NumberTheory.Divisors
import Mathlib.Util.Qq
/-! # Divisor Simprocs
This file implements (d)simprocs to compute various objects related to di... |
linear_combination'.lean | import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Tactic.LinearCombination'
import Mathlib.Tactic.Linarith
set_option autoImplicit true
private axiom test_sorry : ∀ {α}, α
-- We deliberately mock R here so that we don't have to import the deps
axiom Real : Type
notation "ℝ" => Real
@[instance] axiom Real.field... |
Opposite.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.GuitartExact.VerticalComposition
/-!
# The opposite of a Guitart exact square
A `2`-square is Guitart exact iff the opposite (transposed) `2`-sq... |
Theorems.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Tactic.FunProp.Decl
import Mathlib.Tactic.FunProp.Types
import Mathlib.Tactic.FunProp.FunctionData
import Mathlib.Lean.Meta.RefinedDiscrTree.Initialize
i... |
Basic.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Isaac Hernando, Coleton Kotch, Adam Topaz
-/
import Mathlib.Algebra.Homology.ShortComplex.ExactFunctor
import Mathlib.CategoryTheory.Abelian.FunctorCategory
import Mathli... |
Finset.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot
-/
import Mathlib.Data.Finset.Preimage
import Mathlib.Order.Filter.AtTopBot.Tendsto
import Mathlib.Order.Filter.AtTopBot.... |
LeftDerived.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Riccardo Brasca, Adam Topaz, Jujian Zhang, Joël Riou
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.CategoryTheory.Abelian.Projective.Resolution
/-!
# Left-der... |
Auto.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.Algebra.Expr
import Mathlib.Data.Matrix.Reflection
/-! # Automatically generated lemmas for working with concrete matrices
In Mathlib3, this file contained... |
SumProd.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, Patrick Massot
-/
import Mathlib.Topology.Homeomorph.Defs
import Mathlib.Topology.Maps.Basic
import Mathlib.Topology.Separation.SeparatedNhds
/-!
# Dis... |
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