filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Action.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.CategoryTheory.Galois.Examples
import Mathlib.CategoryTheory.Galois.Prorepresentability
/-!
# Induced functor to finite `Aut F`-sets
Any (fiber)... |
orderedzmod.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... |
WithLp.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.Analysis.Normed.Lp.PiLp
import Mathlib.MeasureTheory.SpecificCodomains.Pi
/-!
# Integrability in `WithLp`
We prove that `f : X → PiLp q E` is in `Lᵖ`... |
Eigs.lean | /-
Copyright (c) 2023 Mohanad Ahmed. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mohanad Ahmed
-/
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Eigenvalues are characteristic polynomial roots.
In fields we show that:
*... |
seq.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.
(******************************************************... |
PointsPi.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.AlgebraicGeometry.Morphisms.Immersion
/-!
# `Π Rᵢ`-Points of Schemes
We show that the canonical map `X(Π Rᵢ) ⟶ Π X(Rᵢ)` (`AlgebraicGeometry.pointsPi`)
is ... |
Equiv.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.Hom
import Mathlib.Algebra.Ring.Action.Group
/-!
# Isomorphisms of `R`-algebras
This file defines bundled isomorphisms of `R`-... |
Order.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kenny Lau
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Multiset.ZeroCons
import Mathlib.Order.Directed
/-!
# Finsets of ordered types
-/
universe u v w
va... |
NormalForms.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.AlgebraicGeometry.EllipticCurve.VariableChange
import Mathlib.Algebra.CharP.Defs
/-!
# Some normal forms of elliptic curves
This file defines some normal forms of W... |
Defs.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Deepro Choudhury, Scott Carnahan
-/
import Mathlib.LinearAlgebra.PerfectPairing.Basic
import Mathlib.LinearAlgebra.Reflection
/-!
# Root data and root systems
This file con... |
TensorProduct.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.Colimit.Finiteness
import Mathlib.LinearAlgebra.TensorProduct.DirectLimit
/-!
# Tensor product with direct limit of finitely generated submodules
We sh... |
Basic.lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann, Kyle Miller, Mario Carneiro
-/
import Mathlib.Data.Finset.NatAntidiagonal
import Mathlib.Data.Nat.GCD.Basic
import Mathlib.Data.Nat.BinaryRec
import Mathlib.Logic.F... |
Max.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Order.Synonym
/-!
# Minimal/maximal and bottom/top elements
This file defines predicates for elements to be minimal/maxi... |
ParametrizedAdjunction.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.LiftingProperties.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Adjunction.Parametrized
/-!
# L... |
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.LinearAlgebra.Matrix.Adjugate
import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.RingTheory.MatrixPolynomialAlgebra
/-!
# Characteristic polynomials... |
Basic.lean | /-
Copyright (c) 2020 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Algebra.ContinuedFractions.Basic
import Mathlib.Algebra.Order.Floor.Defs
/-!
# Computable Continued Fractions
## Summary
We formalise the standa... |
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 Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Field.Rat
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.Algebra.GroupWithZero.Un... |
Tietze.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.Analysis.Complex.Basic
import Mathlib.Analysis.RCLike.Lemmas
import Mathlib.Topology.TietzeExtension
import Mathlib.Analysis.NormedSpace.HomeomorphBall
i... |
Testable.lean | /-
Copyright (c) 2022 Henrik Böving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving, Simon Hudon
-/
import Plausible.Testable
import Mathlib.Logic.Basic
/-!
This module contains `Plausible.Testable` and `Plausible.PrintableProb` instances for mathlib typ... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
test_rat.v | From mathcomp Require Import all_boot all_order all_algebra.
Local Open Scope ring_scope.
Goal 2%:Q + 2%:Q = 4%:Q.
Proof. reflexivity. Qed.
Goal - 2%:Q = -1 * 2%:Q.
Proof. reflexivity. Qed.
Goal 2%:Q ^+ 2 = 4%:Q.
Proof. reflexivity. Qed.
Goal (-1)^-1 = -1 :> rat.
Proof. reflexivity. Qed.
Local Open Scope rat_scop... |
ring_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 choice ssrnat.
From mathcomp Require Import seq ssralg generic_q... |
ChevalleyComplexity.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.Order.SuccPred.WithBot
import Mathlib.Algebra.Polynomial.CoeffMem
import Mathlib.Data.DFinsupp.WellFounded
import Mathlib... |
DegLex.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.Algebra.Group.TransferInstance
import Mathlib.Data.Finsupp.MonomialOrder
import Mathlib.Data.Finsupp.Weight
/-! Homogeneous lexicograph... |
Opposite.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton, Simon Hudon, Kenny Lau
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Small.Defs
/-!
# Opposites
In this file we define a structure `Opposite α` con... |
PUnit.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.Algebra.GCDMonoid.Basic
import Mathlib.Algebra.Ring.PUnit
/-!
# `PUnit` is a GCD monoid
This file collects facts about algebraic structures on the one-element ... |
Plus.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.Sites.Sheaf
/-!
# The plus construction for presheaves.
This file contains the construction of `P⁺`, for a presheaf `P : Cᵒᵖ ⥤ D`
where `C` i... |
Born.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.ConcreteCategory.Basic
import Mathlib.Topology.Bornology.Hom
/-!
# The category of bornologies
This defines `Born`, the category of bornol... |
choice.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(**************************************************... |
interval.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 div fintype bigo... |
RingInvo.lean | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow, Kenny Lau
-/
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Algebra.Ring.Opposite
/-!
# Ring involutions
This file defines a ring involution as a structure exte... |
Basic.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Minimal
import Mathlib.Analysis.InnerProductSpace.Symmetric
import Mathlib.Analys... |
ExtensiveTopology.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.Sites.Coherent.Basic
/-!
# Description of the covering sieves of the extensive topology
This file characterises the covering sieve... |
TranslationNumber.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Order.Iterate
import Mathlib.Order.SemiconjSup
import Mathlib.Topology.Order.MonotoneContinuity
import M... |
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, Floris van Doorn
-/
import Mathlib.Algebra.Order.CauSeq.Completion
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Data.Rat.Cast.Defs
/-!
# Real numbers from Cauc... |
BoundedVariation.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.FDeriv.Add
import Mathlib.Analysis.Calculus.FDeriv.Equiv
import Mathlib.Analysis.Calculus.FDeriv.Prod
import Mathlib.Analysis.C... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
Basic.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Algebra.GroupWithZero.Basic
import Mathlib.Algebra.Group.Pointwise.Set.Basic
/-!
# Pointwise operations of sets in a group with zero... |
Lemmas.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker
-/
import Mathlib.Algebra.Divisibility.Hom
import Mathlib.Algebra.Group.Irreducible.Lemmas
import Mathlib.Algebra.GroupWithZero.Equiv
import Mathlib.Alge... |
GluingOneHypercover.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Joël Riou, Ravi Vakil
-/
import Mathlib.AlgebraicGeometry.Gluing
import Mathlib.AlgebraicGeometry.Sites.BigZariski
import Mathlib.CategoryTheory.Sites.OneHypercover
/-!
# The ... |
FunctorCategory.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.Monoidal.FunctorCategory
import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
import Mathlib.CategoryTheory.Functor.Category
import Mathlib.Categ... |
Notation.lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura
-/
import Mathlib.Init
/-!
# Notation `ℕ` for the natural numbers.
-/
@[inherit_doc] notation "ℕ" => Nat
|
Integral.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.RingTheory.IntegralClosure.IntegrallyClosed
import Mathlib.RingTheory.Valuation.Integers
/-!
# Integral elements over the ring of integers of a valuation
The r... |
HasColimits.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Geometry.RingedSpace.LocallyRingedSpace
import Mathlib.Algebra.Category.Ring.Constructions
import Mathlib.Geometry.RingedSpace.OpenImmersion
import Mathlib.C... |
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, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.End
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Algebra.... |
Instances.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.MorphismProperty.WeakFactorizationSystem
import Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
/-!
# Consequences of model cate... |
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.Basic
import Mathlib.Data.Fintype.BigOperators
/-!
# Intervals in a pi type
This file shows that (dependent) functions to locally f... |
Criterion.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Antoine Chambert-Loir
-/
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Polynomial.Content
import Mathlib.RingTheory.Ideal.Quotient.Operations
/-... |
Adjunctions.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.Topology.Category.Stonean.Basic
import Mathlib.Topology.Category.TopCat.Adjunctions
import Mathlib.Topology.Compactification.StoneCech
/-!
# Adjun... |
Monomorphisms.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.MorphismProperty.Limits
import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Monomorphisms are stable under cobase change
In an abelian category `C... |
Centralizer.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.LinearAlgebra.TensorProduct.Basis
import Mathlib.RingTheory.TensorProduct.Basic
/-!
# Properties of centers and centralizers
This file contains theorems ... |
TsumUniformlyOn.lean | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
import Mathlib.Analysis.Calculus.UniformLimitsDeriv
import Mathlib.Analysis.NormedSpace.FunctionSeries
import Math... |
Basic.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.MeasureTheory.Measure.Real
import Mathlib.MeasureTheory.Measure.Typeclasses.Finite
import Mathlib.Topology.Algebra.InfiniteSum.Module
/-!
# Vector valued m... |
DepRewrite.lean | /-
Copyright (c) 2025 Aaron Liu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Liu, Wojciech Nawrocki
-/
import Lean.Elab.Tactic.Simp
import Lean.Elab.Tactic.Conv.Basic
import Lean.Elab.Tactic.Rewrite
import Mathlib.Init
/-! ## Dependent rewrite tactic -/
name... |
Fiber.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.AlgebraicGeometry.PullbackCarrier
import Mathlib.AlgebraicGeometry.Morphisms.Finite
import Mathlib.RingTheory.Spectrum.Prime.Jacobson
/-!
# Scheme-theoretic... |
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.Polynomial.Module.AEval
/-!
# Polynomial module
In this file, we define the polynomial module for an `R`-module `M`, i.e. the `R[X]`-module `M[X]`.... |
TuranDensity.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.Asymptotics.AsymptoticEquivalent
import Mathlib.Combinatorics.Enumerative.DoubleCounting
import Mathlib.Combinatorics.SimpleGraph.DeleteEdge... |
frobenius.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 div.
From mathcomp Require Import fintype bigop prime finset fingroup morphism.
From mathcom... |
finfun.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 tuple.
... |
LaxMilgram.lean | /-
Copyright (c) 2022 Daniel Roca González. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Roca González
-/
import Mathlib.Analysis.InnerProductSpace.Dual
/-!
# The Lax-Milgram Theorem
We consider a Hilbert space `V` over `ℝ`
equipped with a bounded bilinear f... |
Matching.lean | /-
Copyright (c) 2020 Alena Gusakov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alena Gusakov, Arthur Paulino, Kyle Miller, Pim Otte
-/
import Mathlib.Combinatorics.SimpleGraph.Clique
import Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph
import Mathlib.Com... |
Basic.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Combinatorics.Quiver.Basic
/-!
This file defines a few basic properties of groupoids.
-/
namespace CategoryT... |
End.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Andrew Yang
-/
import Mathlib.CategoryTheory.Monoidal.Functor
/-!
# Endofunctors as a monoidal category.
We give the monoidal category structure on `C ⥤ C`,
and show that... |
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... |
PrimeSeparator.lean | /-
Copyright (c) 2024 Sam van Gool. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sam van Gool
-/
import Mathlib.Order.PrimeIdeal
import Mathlib.Order.Zorn
/-!
# Separating prime filters and ideals
In a bounded distributive lattice, if $F$ is a filter, $I$ is an id... |
LogTrigonometric.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic
/-!
# Integral of `log ∘ sin`
This file computes special values of the integral of `log ∘ sin`... |
ssralg.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 choice fintype finf... |
classfun.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... |
wlog.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Johan Commelin
-/
import Mathlib.Tactic.WLOG
import Mathlib.Algebra.Ring.Nat
example {x y : ℕ} : True := by
wlog h : x ≤ y
· guard_hyp h : ¬x ≤ y
guard_hyp this : ∀ ... |
Sequences.lean | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot, Yury Kudryashov
-/
import Mathlib.Order.Filter.AtTopBot.Defs
import Mathlib.Topology.Defs.Filter
/-!
# Sequences in topological spaces
In this f... |
Basic.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. 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.TopCat.Basic
import Mathlib.CategoryTheory.Functor.EpiMono
import Mathlib.Cate... |
Basic.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.Algebra.Group.Submonoid.Operations
import Mathlib.Data.DFinsupp.Sigma
import Mathlib.Data.DFinsupp.Submonoid
/-!
# Direct sum
This file defines the direct sum ... |
ProdUnivMany.lean | import Mathlib.Data.Fin.Tuple.Reflection
@[to_additive]
lemma prod_test (R : Type) [CommMonoid R] (f : Fin 10 → R) :
∏ i, f i = f 0 * f 1 * f 2 * f 3 * f 4 * f 5 * f 6 * f 7 * f 8 * f 9 := by
simp only [Fin.prod_univ_ofNat]
/--
info: sum_test (R : Type) [AddCommMonoid R] (f : Fin 10 → R) :
∑ i, f i = f 0 + f ... |
Defs.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
import Mathlib.Data.FunLike.Equiv
import Mathlib.Data.Quot
import Mathlib.Data.Subtype
import Mathlib.Logic.Unique
import Mathlib.Tactic.Con... |
Embeddings.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Xavier Roblot
-/
import Mathlib.Algebra.Algebra.Hom.Rat
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.NumberTheory.NumberField.Basic
/-!
# Embeddings of... |
Finite.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Pointwise.Set.Scalar
import Mathlib.Data.Finite.Prod
import Mathlib.Algebra.Group.Pointwise.Set.Basic
/-! # Finiteness lemmas for pointwise ... |
Nakayama.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.RingTheory.Finiteness.Defs
import Mathlib.RingTheory.Ideal.Operations
/-!
# Nakayama's lemma
## Main results
* `exists_sub_one_mem_and_smul_eq_zero_... |
PUnit.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.Topology.Sheaves.SheafCondition.Sites
/-!
# Presheaves on `PUnit`
Presheaves on `PUnit` satisfy sheaf condition iff its value at empty set is a terminal ... |
Filter.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Filter
import Mathlib.Topology.Order.Basic
/-!
# Topology on filters of a space with order topology
In this file we prove that `𝓝 (f x)` ... |
Basic.lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kim Morrison
-/
import Mathlib.Algebra.Order.Hom.Monoid
import Mathlib.SetTheory.Game.Ordinal
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module
"This m... |
Matrix.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Eric Wieser
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Matrices as a normed space
In this file we provide the following non-instances for norms on matr... |
Partial.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.Order.Filter.Partial
import Mathlib.Topology.Neighborhoods
/-!
# Partial functions and topological spaces
In this file we prove properties of `Filter.P... |
HVertexOperator.lean | /-
Copyright (c) 2024 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.RingTheory.HahnSeries.Multiplication
/-!
# Vertex operators
In this file we introduce heterogeneous vertex operators using Hahn series. When `R = ℂ`,... |
Module.lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.SetLike.Fintype
import Mathlib.Order.Filter.EventuallyConst
import Mathlib.RingTheory.Ideal.Prod
import Mathlib.RingTheory.Ideal.Quotient.Operations
i... |
Real.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lorenzo Luccioli, Rémy Degenne, Alexander Bentkamp
-/
import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
import Mathlib.MeasureTheory.Group.Convolution
import Mathlib.Pro... |
Pi.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.LinearAlgebra.Finsupp.LSum
import Mathlib.LinearAlgebra.Pi
/-!
# Properties of the module `α →₀ M`
* `Finsupp.linearEquivFunOnFinite`: `α →₀ β` and `... |
RightExactness.lean | /-
Copyright (c) 2023 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Exact
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Ideal.Quotient.Defs
import Mathlib.RingTheory.TensorProduct... |
Basic.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Filippo A. E. Nuccio, Andrew Yang
-/
import Mathlib.RingTheory.Ideal.MinimalPrime.Basic
import Mathlib.RingTheory.Nilpotent.Lemmas
import Mathlib.RingTheory.Noetherian.... |
WithBotTop.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Set.Image
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Order.WithBot
/-!
# Intervals in `WithTop α` and `WithBot α`
In this file we ... |
Basic.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Circle
import Mathlib.Analysis.NormedSpace.BallAction
/-!
# Poincaré disc
In this file we define `Complex.UnitDisc` to be the unit... |
Basic.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang, Fangming Li
-/
import Mathlib.Algebra.DirectSum.Algebra
import Mathlib.Algebra.DirectSum.Decomposition
import Mathlib.Algebra.DirectSum.Internal
... |
DivMod.lean | /-
Copyright (c) 2024 Lean FRO. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Init
/-!
# Basic lemmas about division and modulo for integers
-/
namespace Int
/-! ### `ediv` and `fdiv` -/
theorem mul_ediv_le_mul_ediv_assoc {a : Int}... |
sesquilinear.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup.
From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector.
(************************************************... |
Basic.lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import Mathlib.Data.ENNReal.Real
import Mathlib.Tactic.Bound.Attribute
import Mathlib.Topology... |
SpecificDegree.lean | /-
Copyright (c) 2024 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.Tactic.IntervalCases
import Mathlib.Algebra.Polynomial.FieldDivision
/-!
# Polynomials of specific deg... |
Hausdorff.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.Compactness.SigmaCompact
import Mathlib.Topology.Irreducible
import Mathlib.Topology.Separation.Basic
/-!
# T₂ and T₂.₅ space... |
Integral.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.AlgebraicGeometry.Morphisms.AffineAnd
import Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion
import Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed... |
Descent.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.Affine
import Mathlib.AlgebraicGeometry.Morphisms.AffineAnd
import Mathlib.AlgebraicGeometry.Morphisms.LocalIso
import ... |
algnum.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
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... |
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