filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Structures.lean | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Geometry.Manifold.Algebra.LieGroup
/-!
# `C^n` structures
In this file we define `C^n` structures that build on Lie groups. We prefer using the
t... |
pgroup.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype bigop finset prime fingroup morphism.
From mat... |
QuasiIso.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
import Mathlib.Algebra.Homology.Homotopy
import Mathlib.Algebra.Homology.ShortComplex.Retract
import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
#... |
DomMulAct.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.GroupTheory.GroupAction.DomAct.Basic
/-!
# Topological space structure on `Mᵈᵐᵃ` and `Mᵈᵃᵃ`
In this file ... |
Basic.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.RatFunc.Defs
import Mathlib.RingTheory.Polynomial.Content
import Mathlib.RingTheory.Algebraic.Integral
/-!
# The field structure of rational fun... |
spread.lean | import Mathlib.Tactic.Spread
set_option autoImplicit true
class Foo (α : Type) where
bar : True
class Something where
bar : True
instance : Something where
bar := by trivial
instance : Foo α where
__ := instSomething -- include fields from `instSomething`
example : Foo α := {
__ := instSomething -- inclu... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
MinpolyDiv.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed
import Mathlib.FieldTheory.PrimitiveElement
import Mathlib.FieldTheory.IsAlgClosed.Basic
/-!
# Results about `minpoly... |
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
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Finset.Sum
/-!
# Big operators
In this file we prove theor... |
FreeLocus.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.RingTheory.Flat.Stability
import Mathlib.RingTheory.LocalProperties.Projective
import Mathlib.RingTheory.LocalRing.Module
import Mathlib.RingTheory.Localizat... |
ZagierTwoSquares.lean | /-
Copyright (c) 2023 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan, Thomas Browning
-/
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.Tactic.Linarith
/-!
# Zagier's "one-sentence proof" of Fermat's theorem on sums of two squares
"T... |
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... |
Bornology.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Topology.Bornology.Constructions
/-!
# Bornology of order-bounded sets
This file relates the notion of bornology-boundedness (sets that lie in a bornolog... |
Pigeonhole.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Finset.Union
import Mathlib.Data.Fintype.EquivFin
/-!
# Pigeonhole principles in finite types
## Main declarations
We provide the following ver... |
Basic.lean | /-
Copyright (c) 2022 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.LinearAlgebra.Contraction
import Mathlib.Algebra.Group.Equiv.TypeTags
/-!
# Monoid representations
This file introduces monoid representations and ... |
Basic.lean | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel, Joël Riou
-/
import Mathlib.Algebra.Module.Presentation.Basic
import Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating
/-!
# Exterior powers
We study the exterior power... |
BinPow.lean | import Mathlib.Data.ZMod.Defs
-- A 1024-bit prime number
set_option linter.style.longLine false in
abbrev M : Nat := 0xb10b8f96a080e01dde92de5eae5d54ec52c99fbcfb06a3c69a6a9dca52d23b616073e28675a23d189838ef1e2ee652c013ecb4aea906112324975c3cd49b83bfaccbdd7d90c4bd7098488e9c219a73724effd6fae5644738faa31a4ff55bccc0a151af5f... |
OrderIso.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.Order.GroupWithZero.Unbundled.Basic
import Mathlib.Algebra.GroupWithZero.Units.Equiv
import Mathlib.Order.Hom.Basic
/-!
# Multiplication by a positi... |
Pullback.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.CategoryTheory.Adjunction.Restrict
import Mathlib.CategoryTheory.Functor.Flat
import Mathlib.CategoryTheory.Sites.Continuous
import Mathlib.CategoryTheory.Si... |
Real.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.NNReal.Star
import Mathlib.Topology.Algebra.Star
import Mathlib.Topology.MetricSpace.Pseudo.Constructions
/-!
# Topological prope... |
Refinements.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.Exact
/-!
# Refinements
In order to prove injectivity/surjectivity/exactness properties for diagrams
in the category of abelian g... |
HilbertPoly.lean | /-
Copyright (c) 2024 Fangming Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fangming Li, Jujian Zhang
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Algebra.Polynomial.Eval.SMul
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.Order.Interval... |
Theta.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.Asymptotics.Lemmas
import Mathlib.Analysis.Normed.Module.Basic
/-!
# Asymptotic equivalence up to a constant
In this file we define `Asymp... |
ForgetCorepresentable.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.Grp.Basic
import Mathlib.CategoryTheory.Yoneda
/-!
# The forget functor is corepresentable
It is shown that the forget functor `AddCommGrp.{u}... |
Basic.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Algebra.Notation.Pi.Basic
import Mathlib.Data.Sum.Basic
import Mathlib.Logic.Unique
import Mat... |
Lattice.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Justus Springer
-/
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
import Mathlib.CategoryTheory.Limits.Shapes.Prod... |
Const.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Functor.Multivariate
import Mathlib.Data.QPF.Multivariate.Basic
/-!
# Constant functors are QPFs
Constant functors map every type vectors to the sa... |
Oplax.lean | /-
Copyright (c) 2022 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
import Mathlib.Tactic.CategoryTheory.ToApp
/-!
# Oplax functors
An oplax functor `F` between bicategories `B` and ... |
AB.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.AB
import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf
import Mathlib.Condensed.Light.Epi
/-!
# Grothendieck... |
Basic.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.FieldTheory.Extension
import Mathlib.FieldTheory.Normal.Defs
import Mathlib.FieldTheory.Perfect
import Mathlib.RingTheory.Localization.Integral
/-!
# Algebraica... |
ModuleCat.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory
import Mathlib.Algebra.Category.ModuleCat.Colimits
/-!
# Homology and exactness of short complexes of modules
In... |
FullyFaithful.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.Fractions
import Mathlib.Algebra.Homology.SingleHomology
/-! # The fully faithful embedding of the abelian category in its deri... |
Subring.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.Degree.Support
import Mathlib.Algebra.Polynomial.Eval.Coeff
import Mathlib.Algebra.Ring.Su... |
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.CategoryTheory.Sites.ConstantSheaf
import Mathlib.Condensed.Discrete.LocallyConstant
import Mathlib.Condensed.Light.Module
import Mathlib.Condensed... |
imset2_gproduct.v | From mathcomp Require Import all_boot all_fingroup.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Import GroupScope.
Open Scope group_scope.
Check @ker_sdprodm.
|
finset.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat div seq.
From mathcomp Require Import choice fintype finf... |
FunctionSeries.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.Normed.Group.InfiniteSum
import Mathlib.Topology.Instances.ENNReal.Lemmas
/-!
# Continuity of series of functions
We show that series ... |
TraceForm.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.DirectSum.LinearMap
import Mathlib.Algebra.Lie.InvariantForm
import Mathlib.Algebra.Lie.Weights.Cartan
import Mathlib.Algebra.Lie.Weights.Linear
impo... |
HasNoLoop.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.ComplexShape
import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Algebra.Group.Nat.Defs
/-!
# Complex shapes with no loop
Let `c : ComplexSha... |
Clear_.lean | import Mathlib.Tactic.Clear_
import Mathlib.Tactic.Replace
set_option linter.unusedTactic false
-- Most basic test
example (_delete_this : Nat) : Nat := by
clear_
fail_if_success assumption
exact 0
-- Confirms that clear_ does not delete class instances
example [_dont_delete_this : Inhabited Nat] : Inhabited N... |
ToMatrix.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.LinearAlgebra.Charpoly.Basic
import Mathlib.LinearAlgebra.Matrix.Basis
import Mathlib.RingTheory.Finiteness.Prod
/-!
# Characteristic polynomial
#... |
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... |
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... |
Defs.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.Ring.Defs
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Tactic.DeriveFintype
/-!
# Sign type... |
SuccPred.lean | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Order.SuccPred.Basic
/-!
# Set intervals in a successor-predecessor order
This file proves relations between the ... |
SheafHom.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.CategoryTheory.Sites.Over
/-! Internal hom of sheaves
In this file, given two sheaves `F` and `G` on a site `(C, J)` with values
in a category `A`, we define ... |
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... |
Cast.lean | /-
Copyright (c) 2022 Antoine Labelle, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle, Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Basic
import Mathlib.Combinatorics.Quiver.Path
/-!
# Rewriting arrows and paths along vertex... |
Sieves.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Edward Ayers
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
import Mathlib.Data.Set.BooleanAlgebra
/-!
# Theory of sieves
- For an object `X` of a ca... |
MinImports.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Lean.Elab.DefView
import Lean.Util.CollectAxioms
import ImportGraph.Imports
import ImportGraph.RequiredModules
-- Import this linter explicitly to ensure that
--... |
AssertExists.lean | import Mathlib.Util.AssertExists
/-- info: No assertions made. -/
#guard_msgs in
#check_assertions
#check_assertions!
assert_not_exists Nats
theorem Nats : True := .intro
/--
info:
✅️ 'Nats' (declaration) asserted in 'MathlibTest.AssertExists'.
---
✅️ means the declaration or import exists.
❌️ means the declaratio... |
Dimension.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.Group.Pointwise.Set.Card
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathlib.RingTheory.Adjoin.Basic
/-!
# Some results on dimensions of algeb... |
norm_num_rpow.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, David Renshaw
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
example : (2 : ℝ) ^ (3 : ℝ) = 8 := by norm_num1
example : (1 : ℝ) ^ (20 : ℝ) = 1 := by norm_num1
exa... |
Single.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.GradedObject
/-!
# The graded object in a single degree
In this file, we define the functor `GradedObject.single j : C ⥤ GradedObject J C`
which... |
Opposite.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.Algebra.Algebra.Equiv
import Mathlib.Algebra.Module.Opposite
import Mathlib.Algebra.Ring.Opposite
/-!
# Algebra structures on the multiplicative opposite
#... |
Basic.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.RingTheory.Spectrum.Maximal.Defs
import Mathlib.RingTheory.Spectrum.Prime.Defs
/-!
# Maximal spectrum of a commutative (semi)ring
... |
Bilinear.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Module.LinearMap.End
import Mathlib.Data.Matrix.Mul
import Mathlib.Data.Matrix.Basis
import Mathlib.Algebra.Algebra.Bilinear
/-!
# Bundled versions ... |
Week3P1.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.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Nat.Cast.Field
impo... |
OfNorm.lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Topology.Algebra.Algebra
import Mathlib.Analysis.InnerProductSpace.Convex
import Mathlib.Algebra.Module.LinearMap.Rat
import Mathlib.Tactic.Module
/... |
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.Topology.Defs.Sequences
import Mathlib.Topology.UniformSpace.Cauchy
/-!
# Sequences in topological spaces
In t... |
CompactlySupported.lean | /-
Copyright (c) 2024 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
import Mathlib.Topology.Algebra.Order.Support
import Mathlib.Topology.ContinuousMap.ZeroAtInfty
/-!
# Compactly supported continuous functions
In this file, we define t... |
HomologicalFunctor.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.HomologicalComplexAbelian
import Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit
import Mathlib.Algebra.Homology.HomologySequence
impo... |
Acyclic.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.Combinatorics.SimpleGraph.Connectivity.Connected
import Mathlib.SetTheory.Cardinal.Finite
import Mathlib.Tactic.Linarith
/-!
# Acyclic graphs and trees
Th... |
Perfect.lean | /-
Copyright (c) 2022 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
import Mathlib.Topology.Separation.Regular
/-!
# Perfect Sets
In this file we define perfect subsets of a topological space, and prove some basic properties,
inc... |
ByContra.lean | /-
Copyright (c) 2022 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Batteries.Tactic.Init
import Mathlib.Tactic.Push
/-!
# The `by_contra` tactic
The `by_contra!` tactic is a variant of the `by_contra` tactic, for proofs of con... |
List.lean | /-
Copyright (c) 2021 Stuart Presnell. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stuart Presnell
-/
import Mathlib.Algebra.Order.Ring.Canonical
import Mathlib.Algebra.BigOperators.Group.List.Defs
/-!
# Big operators on a list in ordered rings
This file contains ... |
Localization.lean | /-
Copyright (c) 2021 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import Mathlib.GroupTheory.MonoidLocalization.Basic
import Mathlib.RingTheory.OreLocalization.Ring
import Mathlib.Topology.Algebra.Rin... |
QuadraticReciprocity.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Michael Stoll
-/
import Mathlib.NumberTheory.LegendreSymbol.Basic
import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum
/-!
# Quadratic reciprocity.
## Main r... |
runCmd.lean | import Lean.Elab.Tactic.ElabTerm
open Lean Elab Tactic
example : True := by
run_tac
evalApplyLikeTactic MVarId.apply (← `(True.intro))
example : True := by_elab
Term.elabTerm (← `(True.intro)) none
|
Mul.lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Anatole Dedecker, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Mul
import Mathlib.Analysis.Calculus.FDeriv.Add
... |
ChartedSpace.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.Topology.PartialHomeomorph
import Mathlib.Topology.Connected.LocPathConnected
/-!
# Charted spaces
A smooth manifold is a topological space `M`... |
Analytic.lean | /-
Copyright (c) 2024 Geoffrey Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Geoffrey Irving
-/
import Mathlib.Analysis.Analytic.Composition
import Mathlib.Analysis.Analytic.Constructions
import Mathlib.Analysis.Complex.CauchyIntegral
import Mathlib.Analysis.S... |
Rayleigh.lean | /-
Copyright (c) 2023 Jason Yuen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jason Yuen
-/
import Mathlib.Data.Real.ConjExponents
import Mathlib.Data.Real.Irrational
/-!
# Rayleigh's theorem on Beatty sequences
This file proves Rayleigh's theorem on Beatty sequen... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
SupInf.lean | import Mathlib
/-- info: max 1 2 : ℕ -/
#guard_msgs in
#check max (1 : ℕ) 2
/-- info: max 1 2 : ℝ -/
#guard_msgs in
#check max (1 : ℝ) 2
/-- info: ({0} ⊔ {1} ⊔ ({2} ⊔ {3})) ⊓ ({4} ⊔ {5}) ⊔ {6} ⊓ {7} ⊓ ({8} ⊓ {9}) : Set ℕ -/
#guard_msgs in
#check (max (min (max (max {0} {1}) (max {2} {3})) (max {4} {5})) (min (min {... |
Opposite.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.Functor
import Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence
/-!
# Monoidal opposites
We write `Cᵐᵒᵖ` for the monoidal opp... |
Basic.lean | /-
Copyright (c) 2024 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.PowerSeries.Basic
import Mathlib.Combinatorics.Enumerative.B... |
SelbergSieve.lean | /-
Copyright (c) 2024 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.NumberTheory.ArithmeticFunction
/-!
# The Selberg Sieve
We set up the working assumptions of the Selber... |
ZetaAsymp.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.NumberTheory.LSeries.RiemannZeta
import Mathlib.NumberTheory.Harmonic.GammaDeriv
/-!
# Asymptotics of `ζ s` as `s → 1`
The goal of this file is to ev... |
InvSubmonoid.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.GroupTheory.Submonoid.Inverses
import Mathlib.RingTheory.FiniteType
import Mathlib.RingTheory.Loc... |
IncidenceAlgebra.lean | /-
Copyright (c) 2022 Alex J. Best, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Yaël Dillies
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Module.BigOperators
import Mathlib.... |
ToLevel.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Tactic.PPWithUniv
/-! # `ToLevel` class
This module defines `Lean.ToLevel`, which is the `Lean.Level` analogue to `Lean.ToExpr`.
**Warning:** Import `Math... |
fingraph.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.
From mathcomp Require Import seq path fintype.
(******************************************... |
GroupTopology.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.Algebra.Group.Basic
/-!
### Lattice of group topologies
We define a type class `GroupTopology α` which endow... |
RestrictScalars.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
/-!
# The derivative of the scalar restriction of a linear map
For detailed document... |
Bimod.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Oleksandr Manzyuk
-/
import Mathlib.CategoryTheory.Bicategory.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equali... |
CoeffList.lean | /-
Copyright (c) 2023 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
import Mathlib.Algebra.Polynomial.Degree.Definitions
import Mathlib.Algebra.Polynomial.EraseLead
import Mathlib.Data.List.Range
/-!
# A list of coefficients of a polynom... |
Unramified.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.NumberTheory.RamificationInertia.Basic
import Mathlib.RingTheory.Unramified.LocalRing
import Mathlib.RingTheory.LocalRing.ResidueField.Algebraic
/-!
# Unra... |
Sum.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.Option.Defs
import Mathlib.Data.Sigma.Basic
import Mathlib.Logic.Equiv.Prod
import Mathlib.Tactic.Coe
/-!
# Equivalence... |
Defs.lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.Map
/-!
# Definitions about invariant measures
In this file we define typeclasses for measures invariant u... |
Cardinal.lean | /-
Copyright (c) 2021 Chris Hughes, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Data.Finsupp.Fintype
import Mathlib.SetTheory.Cardinal.Finsupp
/-!
# Cardinality of Multiv... |
Imo2006Q3.lean | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib.Analysis.SpecialFunctions.Sqrt
import Mathlib.Tactic.Polyrith
/-!
# IMO 2006 Q3
Determine the least real number $M$ such that
$$
\left| ab(a^2 - b^2) + bc(b^2 ... |
presentation.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq.
From mathcomp Require Import fintype finset fingroup morphism.
(**********************... |
SingleObj.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.Endomorphism
import Mathlib.CategoryTheory.FinCategory.Basic
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.Algebra.Categor... |
Basic.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.Ring.Prod
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Ring.Canonical
import Mathlib.Order.Interval.Basic
im... |
CompareExp.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.SpecialFunctions.Pow.Asymptotics
import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
import Mathlib.Analysis.Asymptotics.SpecificAsympt... |
FiniteSupport.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.Algebra.Notation.Support
import Mathlib.Data.Set.Finite.Basic
/-!
# Finiteness of support
-/
assert_not_exists Monoid
namespace Function
variable {α β γ :... |
Retract.lean | /-
Copyright (c) 2024 Jack McKoen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jack McKoen
-/
import Mathlib.CategoryTheory.Retract
import Mathlib.CategoryTheory.MorphismProperty.Basic
/-!
# Stability under retracts
Given `P : MorphismProperty C`, we introduce a t... |
finiteness.lean | import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
import Mathlib.Data.ENNReal.Inv
import Mathlib.MeasureTheory.Measure.Typeclasses.Finite
import Mathlib.Tactic.Finiteness
open MeasureTheory Set
open scoped ENNReal NNReal
example : (1 : ℝ≥0∞) < ∞ := by finiteness
example : (3 : ℝ≥0∞) ≠ ∞ := by finiteness
example (a... |
Order.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.Contract
/-!
# Matroid Minors
A matroid `N = M ／ C ＼ D` obtained from a matroid `M` by a contraction then a delete,
(or equivalently, ... |
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