filename stringlengths 5 42 | content stringlengths 15 319k |
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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... |
Expand.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.Algebra.MvPolynomial.Monad
/-!
## Expand multivariate polynomials
Given a multivariate polynomial `φ`, one may replace every occurre... |
fieldext.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 div.
From mathcomp Require Import choice fintype tupl... |
ModEq.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.Algebra.Order.Group.Unbundled.Int
import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.Int.GCD
import Mathlib.Data.Nat.GCD.Basic
/-!
# Congruences modu... |
Subcomplex.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
import Mathlib.CategoryTheory.Subpresheaf.Basic
/-!
# Subcomplexes of a simplicial set
Given a simplicial set `X`, this f... |
Interval.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.Interval.Finset.Nat
import Mathlib.Data.PNat.Defs
/-!
# Finite intervals of positive naturals
This file proves that `ℕ+` is a `LocallyFiniteOrder` ... |
Star.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Nicolò Cavalleri
-/
import Mathlib.Topology.Algebra.Star
import Mathlib.Algebra.Star.StarAlgHom
import Mathlib.Topology.ContinuousMap.Algebra
/-!
# Star structures on cont... |
fraction.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 div seq.
From mathcomp Require Import ssrAC choice tuple ... |
Equitable.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.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Ring.Defs
/-!
# Equitable functions
This file defines eq... |
Subfield.lean | /-
Copyright (c) 2023 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Field.Subfield.Basic
import Mathlib.Data.W.Cardinal
import Mathlib.Tactic.FinCases
/-!
# Cardinality of the division ring generated by a set
`Subfield.... |
Orthogonal.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kexing Ying
-/
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.LinearAlgebra.BilinearForm.Properties
/-!
# Bilinear form
This file defines ort... |
Union.lean | /-
Copyright (c) 2025 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.Lattice
import Mathlib.Data.Set.Card
import Mathlib.LinearAlgebra.Dual.Defs
import Mathlib.Tactic.Module
/-!
# Unions of `Submodule... |
ssrnat.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Import PosDef.
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype.
#[export] Set Warnings "-ov... |
closed_field.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype generic_... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
Group.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.ConditionallyCompleteLattice.Indexed
import Mathlib.Algebra.Order.Group.Unbundled.Basic
import Mathlib.Algebra.Order.Monoid.Unbundled.Order... |
hall.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 choice.
From mathcomp Require Import fintype finset prime fingroup morphism.
From ma... |
generic_quotient.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 choice.
From mathcomp Require Import seq fintype.
(*****... |
CommSq.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
import Mathlib.CategoryTheory.Comma.Arrow
/-!
# Commutative squares
This file provide an API for commutative squares in categories.
If `top`, `left`, `right`... |
Over.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
import Mathlib.CategoryTheory.Limits.MorphismProperty
/-!
# Covers of schemes over a base
In this file... |
MellinInversion.lean | /-
Copyright (c) 2024 Lawrence Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lawrence Wu
-/
import Mathlib.Analysis.Fourier.Inversion
import Mathlib.Analysis.MellinTransform
/-!
# Mellin inversion formula
We derive the Mellin inversion formula as a consequence o... |
Basic.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.ObjectProperty.Shift
import Mathlib.CategoryTheory.Triangulated.Pretriangulated
/-!
# t-structures on triangulated categories
This files introdu... |
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.Analysis.NormedSpace.OperatorNorm.Mul
/-!
# Unitization norms
Given a not-necessarily-unital normed `𝕜`-al... |
GuardGoalNums.lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Init
import Lean.Elab.Tactic.Basic
/-!
A tactic stub file for the `guard_goal_nums` tactic.
-/
open Lean Meta Elab Tactic
/-- `guard_goal_nums n... |
GrpWithZero.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.Algebra.Category.MonCat.Basic
import Mathlib.Algebra.GroupWithZero.WithZero
import Mathlib.CategoryTheory.Category.Bipointed
/-!
# The category of groups ... |
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, Patrick Massot
-/
import Mathlib.Data.Rel
import Mathlib.Order.Filter.SmallSets
import Mathlib.Topology.UniformSpace.Defs
import Mathlib.Topology.Contin... |
Contract.lean | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Minor.Delete
import Mathlib.Tactic.TautoSet
/-!
# Matroid Contraction
Instead of deleting the the elements of `X : Set α` from `M : Matroid ... |
Set.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.Data.Fintype.EquivFin
/-!
# Lemmas about `Finite` and `Set`s
In this file we prove two lemmas about `Finite` and `Set`s.
## Tags
finiteness, finite sets
... |
AEMeasurable.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.Function.LpSeminorm.Trim
import Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp
/-! # Functions a.e. measurable with respect to a sub-σ... |
Module.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.Algebra.DirectSum.Basic
import Mathlib.LinearAlgebra.DFinsupp
import Mathlib.LinearAlgebra.Basis.Defs
/-!
# Direct sum of modules
The first part of the file pr... |
VectorSpace.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.FreeAbelianGroup.Finsupp
import Mathlib.Algebra.MonoidAlgebra.Defs
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Basis.D... |
Star.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.Algebra.GroupWithZero.Action.Pointwise.Set
import Mathlib.Algebra.Module.LinearMap.Prod
import Mathlib.Algebra.Order.Module.Synonym
import Mathlib.Analysis... |
MutuallySingular.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.Restrict
/-! # Mutually singular measures
Two measures `μ`, `ν` are said to be mutually singular (`MeasureTheory.Mea... |
RegularWreathProduct.lean | /-
Copyright (c) 2025 Francisco Silva. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Francisco Silva
-/
import Mathlib.GroupTheory.Sylow
import Mathlib.Algebra.Group.PUnit
import Mathlib.Data.Finite.Perm
import Mathlib.Algebra.Group.End
/-!
# Regular wreath product
... |
AsLimit.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
import Mathlib.Topology.Category.Profinite.Basic
import Mathlib.Topology.DiscreteQuotient
/-!
# Profinite sets as limits of finite sets.
We show that any profi... |
Defs.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.Order.ToIntervalMod
import Mathlib.Algebra.Ring.AddAut
import Mathlib.Data.Nat.Totient
import Mathlib.GroupTheory.Divisible
import Mathlib.Topology.A... |
LinearLocallyFinite.lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Countable.Basic
import Mathlib.Data.Finset.Max
import Mathlib.Data.Fintype.Pigeonhole
import Mathlib.Logic.Enco... |
Coeff.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Polynomial.Coeff
import Mathlib.Algebra.Polynomial.Eval.Defs
/-!
# Evaluation of polynomials
This f... |
Basic.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Discrete
import Mathlib.CategoryTheory.Monoidal.NaturalTransformation
import Mathlib.CategoryTheory.Monoidal.Opposite
import Mathli... |
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... |
Instances.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.MeasurableSpace.Defs
import Mathlib.GroupTheory.GroupAction.IterateAct
import Mathlib.Data.Rat.Init
import Mathlib.Data.Z... |
GaussSum.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic
import Mathlib.NumberTheory.GaussSum
/-!
# Quadratic characters of finite fields
Further facts relying ... |
maximal.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 choice.
From mathcomp Require Import div fintype finfun bigop finset prime binomial.
Fro... |
mxpoly.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 choice seq.
From mathcomp Require Import div fintype tupl... |
Cones.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Kim Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.Functor.Const
import Mathlib.CategoryTheory.Discrete.Basic
import Mathlib.CategoryTheory.Yoneda
import Mat... |
Factors.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.Data.List.Iterate
import Mathlib.GroupTheory.Perm.Cycle.Basic
import Mathlib.GroupTheory.NoncommPiCoprod
import Mathlib.Tactic.Group
/-!
# ... |
Basic.lean | /-
Copyright (c) 2024 Kyle Miller, Jack Cheverton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Jack Cheverton, Jeremy Tan
-/
import Mathlib.Order.CompleteBooleanAlgebra
import Mathlib.Data.Fintype.Pi
/-!
# Digraphs
This module defines directed graphs ... |
SubDPIdeal.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
import Mathlib.RingTheory.DividedPowers.DPMorphism
import Mathlib.RingTheory.Ideal.Quot... |
Pi.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
import Mathlib.Analysis.Calculus.FDeriv.Pi
import Mathlib.Analysis.Calculus.Deriv.Basic
/-!
# One-dimensional derivatives on pi-types.
-/
varia... |
CompleteMultipartite.lean | /-
Copyright (c) 2024 John Talbot and Lian Bremner Tattersall. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: John Talbot, Lian Bremner Tattersall
-/
import Mathlib.Combinatorics.SimpleGraph.Coloring
import Mathlib.Combinatorics.SimpleGraph.Hasse
/-!
# Complete Multip... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
Sub.lean | /-
Copyright (c) 2022 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich
-/
import Mathlib.MeasureTheory.Measure.Typeclasses.Finite
/-!
# Subtraction of measures
In this file we define `μ - ν` to be the least measure `τ` such that `μ ≤ ... |
Basic.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.SmallObject.IsCardinalForSmallObjectArgument
/-!
# The small object argument
Let `C` be a category. A class of morphisms `I : MorphismProperty C... |
PushoutI.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.GroupTheory.CoprodI
import Mathlib.GroupTheory.Coprod.Basic
import Mathlib.GroupTheory.Complement
/-!
## Pushouts of Monoids and Groups
This file defin... |
MulExpNegMulSqIntegral.lean | /-
Copyright (c) 2025 Jakob Stiefel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Stiefel
-/
import Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq
import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
import Mathlib.MeasureTheory.Integral.BoundedContinuo... |
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
-/
import Mathlib.Data.W.Basic
/-!
# Polynomial Functors
This file defines polynomial functors and the W-type construction as a polynomial functor.
(For the M-type const... |
L1.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.MeasureTheory.Integral.SetToL1
/-!
# Bochner integral
The Bochner integral extends the definition of ... |
MkProof.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Miyahara Kō
-/
import Mathlib.Tactic.CC.Datatypes
import Mathlib.Tactic.CC.Lemmas
import Mathlib.Tactic.Relation.Rfl
import Mathlib.Tactic.Relation.Symm
/-!
... |
Multinomial.lean | /-
Copyright (c) 2022 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Pim Otte
-/
import Mathlib.Algebra.Order.Antidiag.Pi
import Mathlib.Data.Finsupp.Multiset
import Mathlib.Data.Nat.Choose.Sum
import Mathlib.Data.Nat.Factorial.BigOperators
impor... |
Operations.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Patrick Massot
-/
import Mathlib.Algebra.Algebra.Subalgebra.Operations
import Mathlib.Algebra.Ring.Fin
import Mathlib.LinearAlgebra.Quotient.Basic
import Mathlib.RingTheory.Ideal... |
Riemannian.lean | /-
Copyright (c) 2025 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.InnerProductSpace.LinearMap
import Mathlib.Topology.VectorBundle.Constructions
import Mathlib.Topology.VectorBundle.Hom
/-! # Riemannia... |
External.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.Int.Order.Units
import Mathlib.Data.ZMod.IntUnitsPower
import Mathlib.RingTheory.TensorProduct.Basic
import Mathlib.LinearAlgebra.DirectSum.TensorProduc... |
UpperLower.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.Algebra.Group.Action.Pointwise.Set.Basic
import Mathlib.Algebra.Group.Pointwise.Set.Lattice
import Mathlib.Algebra.Order.Group.Defs
import Mathlib.Algebra.... |
FiniteDimensional.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.LinearAlgebra.Multilinear.Curry
import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix
/-! # Multilinear maps over finite dimensional spaces
The main result... |
MinimalAxioms.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.MinimalAxioms
/-!
# Minimal Axioms for a Field
This file defines constructors to define a `Field` structu... |
UpperLowerSetTopology.lean | /-
Copyright (c) 2023 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Topology.AlexandrovDiscrete
import Mathlib.Topology.ContinuousMap.Basic
import Mathlib.Topology.Order.LowerUpperTopology
/-!
# Upper and lower... |
Isometric.lean | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric
/-! # ... |
Defs.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs
/-!
# Integral algebras
## Main definitions
Let `R` be a `CommRing` and let `A` be an R-algebra.
* `Algebra.IsInte... |
FiniteType.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.FreeAlgebra
import Mathlib.RingTheory.Adjoin.Polynomial
import Mathlib.RingTheory.Adjoin.Tower
import Mathlib.RingTheory.Ideal.Quotient.Operati... |
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... |
Extensions.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.Algebra.Homology.ShortComplex.ShortExact
import Mathlib.CategoryTheory.ObjectProperty.Basic
/-!
# Properties of objects that are closed under extensions
Given ... |
SnakeLemma.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.ExactSequence
import Mathlib.Algebra.Homology.ShortComplex.Limits
import Mathlib.CategoryTheory.Abelian.Refinements
/-!
# The snake lemma
The ... |
ContinuousMonoidHom.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Nailin Guan
-/
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Topology.Algebra.Group.Defs
/-!
# Continuous Monoid Homs
This file defines the space of cont... |
EpiMono.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.Colimits
import Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits
/-!
# Epimorphisms and monomorphisms in the category of ... |
Function.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import Mathlib.Data.Set.Prod
import Mathlib.Data.Set.Restrict
/-!
# Functions over sets
This file contains... |
Cauchy.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.Topology.Algebra.Constructions
import Mathlib.Topology.Bases
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Topology.UniformSpac... |
Piecewise.lean | /-
Copyright (c) 2025 Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Horner
-/
import Mathlib.Analysis.Convex.Function
/-!
# Convex and concave piecewise functions
This file proves convex and concave theorems for piecewise functions.
## Mai... |
ParallelPair.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.Comma.Final
import Mathlib.CategoryTheory.Limits.Indization.IndObject
/-!
# Parallel pairs of natural transformations between ind-objects... |
Arg.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.Analysis.InnerProductSpace.Convex
import Mathlib.Analysis.SpecialFunctions.Complex.Arg
/-!
# Rays in the complex numbers
This file links the definiti... |
polyXY.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype tuple fi... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
CondexpL1.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.Function.ConditionalExpectation.CondexpL2
import Mathlib.MeasureTheory.Measure.Real
/-! # Conditional expectation in L1
This file contains ... |
Equiv.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Traversable.Lemmas
import Mathlib.Logic.Equiv.Defs
import Batteries.Tactic.SeqFocus
/-!
# Transferring `Traversable` instances along isomorphisms
T... |
Cardinal.lean | /-
Copyright (c) 2025 Peter Nelson and Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Junyan Xu
-/
import Mathlib.Data.Matroid.Map
import Mathlib.Data.Matroid.Rank.ENat
import Mathlib.Data.Matroid.Rank.Finite
import Mathlib.SetTheory.Cardinal.A... |
HasConicalPullbacks.lean | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl
-/
import Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits
/-!
# Existence of conical pullbacks
-/
universe w v' v u u'
namespace Cate... |
ChevalleyWarning.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.FieldTheory.Finite.Basic
/-!
# The Chevalley–Warning theorem
This file contains a proof of the Chevalley–Warning theorem.
Throughout most of this fil... |
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... |
cc.lean | import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Ring.Defs
import Mathlib.Data.Set.Insert
import Mathlib.Data.Vector.Defs
import Mathlib.Tactic.CC
set_option linter.unusedVariables false
/--
warning: The tactic `cc` is deprecated since 2025-07-31, please use `grind` instead.
Please report any regressions at... |
Finsupp.lean | /-
Copyright (c) 2024 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.BigOperators.Finsupp.Basic
import Mathlib.Algebra.Group.Subgroup.Lattice
/-! # Connection between `Subgroup.closure` and `Finsupp.prod` -/
assert... |
Bundled.lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.ModelTheory.ElementarySubstructures
import Mathlib.CategoryTheory.ConcreteCategory.Bundled
/-!
# Bundled First-Order Structures
This file bundles typ... |
Log.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.Order.Floor.Semiring
import Mathlib.Data.Nat.Log
/-!
# Integer logarithms in a field with respect to a natural base
This file defines two `ℤ`-value... |
test_ssrAC.v | From mathcomp Require Import all_boot ssralg.
Section Tests.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite orbACA. Abort.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort.
Lemma ... |
import_all.lean | import Lean
import Std
import Qq
import Batteries
import Aesop
import ProofWidgets
import Mathlib
import Plausible
/-!
Verify that Mathlib and all its upstream dependencies can be simultaneously imported.
We don't `import Cli` or `import ImportGraph` here as these are only used by scripts,
and may not have been built... |
Subgroup.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.Group.Action.End
import Mathlib.Algebra.Group.Subgroup.Finite
import Mathlib.Data.Fintype.Perm
/-!
# Lemmas about subgroups within the permutations ... |
AdjointFunctorTheorems.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow.Small
import Mathlib.CategoryTheory.Generator.Basic
import Mathlib.CategoryTheory.Limits.ConeCategory
import Mathlib.C... |
Finsupp.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Antoine Chambert-Loir
-/
import Mathlib.Algebra.DirectSum.Finsupp
import Mathlib.LinearAlgebra.DirectSum.TensorProduct
import Mathlib.LinearAlgebra.Finsupp.SumProd
/-!... |
Functor.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Simon Hudon, Kenny Lau
-/
import Mathlib.Data.Multiset.Bind
import Mathlib.Control.Traversable.Lemmas
import Mathlib.Control.Traversable.Instances
/-!
# F... |
ContinuousAffineMap.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.Normed.Affine.Isometry
import Mathlib.Topology.Algebra.ContinuousAffineMap
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
/-!
# Conti... |
Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.MeasureTheory.Function.SimpleFunc
/-!
# Lower Lebesgue integral for `ℝ≥0∞`-valued functions
We define the lower Lebesgue integral of ... |
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, Chris Hughes, Mario Carneiro
-/
import Mathlib.Algebra.Ring.Action.End
import Mathlib.RingTheory.Finiteness.Cardinality
import Mathlib.RingTheory.LocalRing.ResidueField.Defs
impo... |
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