filename stringlengths 5 30 | content stringlengths 22 296k |
|---|---|
HasConicalLimits.lean | /-
Copyright (c) 2025 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster, Dagur Asgeirsson, Emily Riehl
-/
import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
import Mathlib.CategoryTheory.Limits.Final
/-!
# Existence of conical limits
This fil... |
CubingACube.lean | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Order.Interval.Set.Group
import Mathlib.Data.Real.Basic
import Mathlib.Data.Set.Finite.Lemmas
import Mathlib.Order.Interval.Set.Disjoint
/... |
cyclic.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 bigo... |
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.RingTheory.MvPolynomial.MonomialOrder
import Mathlib.Data.Finsupp.MonomialOrder.DegLex
/-! # Some lemmas about the deglex monomial order... |
DenselyOrdered.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Order.Interval.Finset.Basic
/-!
# Linear locally finite orders are densely ordered iff they are trivial
## Main results
* `LocallyFiniteOrder.dense... |
Curry.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Fintype.Sort
import Mathlib.LinearAlgebra.Multilinear.Basic
/-!
# Currying of multilinear maps
We register isomorphisms corresponding to cu... |
VectorField.lean | /-
Copyright (c) 2024 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.Symmetric
/-!
# Vector fields in vector spaces
We study functions of the form `V : E → E` on a vector space, thinking ... |
Fold.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Sean Leather
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.FreeMonoid.Basic
import Mathlib.Control.Traversable.Instances
import Mathlib.Control.Traversable.... |
ExtendFrom.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Anatole Dedecker
-/
import Mathlib.Topology.Separation.Regular
/-!
# Extending a function from a subset
The main definition of this file is `extendFrom A f` where `... |
ValuedCSP.lean | import Mathlib.Algebra.Order.AbsoluteValue.Basic
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Combinatorics.Optimization.ValuedCSP
import Mathlib.Data.Fin.Tuple.Curry
import Mathlib.Data.Fin.VecNotation
import Mathlib.Tactic.Positivity
/-!
# VCSP examples
This file shows two simple examples of General-Valued ... |
Subobject.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Subobject.Limits
import Mathlib.CategoryTheory.Abelian.Basic
/-!
# Equivalence between subobjects and quotients in an abelian category
-... |
Pointwise.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Star.Basic
import Mathlib.Data.Set.Finite.Basic
import Mathlib.Data.Set.Lattice.Image
import Mathlib.Algebra.Group.Pointwise.Set.Basic
/-!
# Poi... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
CircleMap.lean | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Fabrizio Barroero, Christopher Hoskin
-/
import Mathlib.Analysis.SpecialFunctions.Complex.Log
import Mathlib.Order.Interval.Set.Defs
/-!
# circleMap
This file def... |
Log.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Benjamin Davidson
-/
import Mathlib.Analysis.SpecialFunctions.Complex.Arg
import Mathlib.Analysis.SpecialFunctions.Log.Basic... |
zmodp.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool choice eqtype ssrnat seq.
From mathcomp Require Import div fintype bigo... |
Substructures.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Gabin Kolly
-/
import Mathlib.Data.Fintype.Order
import Mathlib.Order.Closure
import Mathlib.ModelTheory.Semantics
import Mathlib.ModelTheory.Encoding
/-!
# First-Orde... |
Sum.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.Faithful
/-!
# Sum instances for additive and multiplicative actions
This file defines instances for additive and multiplicative act... |
Ext.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kim Morrison
-/
import Mathlib.Algebra.Group.Finsupp
import Mathlib.Algebra.Group.Submonoid.Basic
import Mathlib.Algebra.Group.TypeTags.Hom
/-!
# Extensionality for ma... |
Square.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.Limits.Shapes.Pullback.Square
import Mathlib.CategoryTheory.Limits.Yoneda
import Mathlib.CategoryTheory.Limits.Preserves.Ulift
/-!
# Preservation... |
GCD.lean | /-
Copyright (c) 2018 Guy Leroy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sangwoo Jo (aka Jason), Guy Leroy, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Semiconj
import Mathlib.Algebra.Group.Commute.Units
import Mathlib.Data.Set.Operati... |
Real.lean | /-
! This file was ported from Lean 3 source file `test/real.lean`
! leanprover-community/mathlib commit d7943885503965d07ccaeb390d65fbc3f45962e6
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathlib.Data.Real.Basic
private axiom test_sorry : ∀ {α}, α... |
ScottContinuity.lean | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Order.Bounds.Basic
/-!
# Scott continuity
A function `f : α → β` between preorders is Scott continuous (referring to Dana Scott) if it
distri... |
Regular.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.Tactic.StacksAttribute
import Mathlib.Topology.Compactness.Lindelof
import Mathlib.Topology.Separation.Hausdorff
import Mathlib.Topolog... |
PWO.lean | /-
Copyright (c) 2022 Alex J. Best. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best
-/
import Mathlib.Order.Preorder.Finsupp
import Mathlib.Order.WellFoundedSet
/-!
# Partial well ordering on finsupps
This file contains the fact that finitely supported fu... |
eqtype.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.
(********************************************************************... |
TensorProduct.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.LinearAlgebra.BilinearForm.Hom
import Mathlib.LinearAlgebra.Dual.Lemmas
import Mathlib.LinearAlgebra.TensorProduct.Tower
import Mathlib.RingTheory.TensorProd... |
PerfectNumbers.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.NumberTheory.ArithmeticFunction
import Mathlib.NumberTheory.LucasLehmer
import Mathlib.Tactic.NormNum.Prime
/-!
# Perfect Numbers
This file proves Th... |
Bernoulli.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kevin Buzzard
-/
import Mathlib.Algebra.BigOperators.Field
import Mathlib.RingTheory.PowerSeries.Inverse
import Mathlib.RingTheory.PowerSeries.WellKnown
/-!
# Bernoull... |
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.
(**********************... |
Prod.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
-/
import Mathlib.MeasureTheory.MeasurableSpace.Embedding
import Mathlib.MeasureTheory.PiSystem
/-!
# The product sigma algebra
This file talks about the measurabi... |
Units.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Units
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Multiplicative actions wi... |
Elements.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Elements
import Mathlib.CategoryTheory.Limits.Types.Limits
import Mathlib.CategoryTheory.Limits.Creates
import Mathlib.CategoryTheory.Limi... |
TopComparison.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.Condensed.Light.Basic
import Mathlib.Condensed.TopComparison
/-!
# The functor from topological spaces to light condensed sets
We define the fun... |
IsConnected.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.Data.List.Chain
import Mathlib.CategoryTheory.PUnit
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.Category.ULift
... |
Prod.lean | /-
Copyright (c) 2018 Simon Hudon. 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.GroupWithZero.Action.Prod
import Mathlib.Algebra.Module.Defs
/-!
# Prod instances for module and multiplicative actions... |
HurwitzZetaValues.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.ZetaValues
import Mathlib.NumberTheory.LSeries.RiemannZeta
/-!
# Special values of Hurwitz and Riemann zeta functions
This file gives t... |
Curry.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.LinearAlgebra.Alternating.Basic
import Mathlib.LinearAlgebra.Multilinear.Curry
/-!
# Currying alternating forms
In this file we define `AlternatingMap.curr... |
ZModChar.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.Data.Int.Range
import Mathlib.Data.ZMod.Basic
import Mathlib.NumberTheory.MulChar.Basic
/-!
# Quadratic characters on ℤ/nℤ
This file defines some quadr... |
SimpIntro.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Elab.Tactic.Simp
import Mathlib.Init
/-! # `simp_intro` tactic -/
namespace Mathlib.Tactic
open Lean Meta Elab Tactic
/--
Main loop of the `simp_intro`... |
test_order_conv.v | From mathcomp Require Import all_boot all_order.
Import Order.Theory.
Section dual_of_dual.
Context (disp : Order.disp_t).
Let eq_dual_dual_preorderType (T : preorderType disp) :
Order.Preorder.on T = Order.Preorder.on T^d^d := erefl.
Let eq_dual_dual_porderType (T : porderType disp) :
Order.POrder.on T = Order.... |
Language.lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson, Martin Dvorak
-/
import Mathlib.Algebra.Order.Kleene
import Mathlib.Algebra.Ring.Hom.Defs
import Mathlib.Data.Set.Lattice
import Mathlib.Tactic.DeriveFintype
/-!
# Languages... |
Basic.lean | /-
Copyright (c) 2019 Neil Strickland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Neil Strickland, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.Semiconj.Basic
/-!
# Additional lemmas about commuting pairs of elements in... |
intdiv.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
RCLike.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.RCLike.Lemmas
import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex
/-!
# Measurability of the basic `RCLike` functions
-/
nonco... |
ContinuousFunctions.lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.MeasureTheory.Function.LpSpace.Basic
import Mathlib.MeasureTheory.Measure.O... |
Instances.lean | /-
Copyright (c) 2024. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: euprunin
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.RingTheory.NonUnitalSubring.Defs
import Mathlib.RingTheory.TwoSidedIdeal.Basic
/-!
# Additional instances for two sided ideals.
-/
instanc... |
Quandle.lean | /-
Copyright (c) 2020 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Algebra.Group.End
import Mathlib.Data.ZMod.Defs
import Mathlib.Tactic.Ring
/-!
# Racks and Quandles
This file defines racks and quandles, algebraic structu... |
Bounds.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.ModularForms.JacobiTheta.TwoVariable
/-!
# Asymptotic bounds for Jacobi theta functions
The goal of this file is to establish some tech... |
HSpaces.lean | /-
Copyright (c) 2022 Filippo A. E. Nuccio Mortarino Majno di Capriglio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Junyan Xu
-/
import Mathlib.Topology.CompactOpen
import Mathlib.Topology.Homotopy.Basic
import Mathlib.Topology.Path
/-!
# H-s... |
fingroup.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 fintype div path... |
UniformFilterBasis.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Algebra.FilterBasis
import Mathlib.Topology.Algebra.IsUniformGroup.Defs
/-!
# Uniform properties of neighborhood bases in topological algebra... |
Use.lean | /-
Copyright (c) 2022 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Gabriel Ebner, Kyle Miller
-/
import Mathlib.Tactic.WithoutCDot
import Lean.Meta.Tactic.Util
import Lean.Elab.Tactic.Basic
/-!
# The `use` tactic
The `use` and `use!`... |
MoveAdd.lean | import Mathlib.Tactic.MoveAdd
import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.Nat.Basic
universe u
variable {R : Type u}
section add
section semigroup
variable [AddCommSemigroup R] {a b c d e f g h : R}
example (h : a + b + c = d) : b + (a + c) = d := by
move_add [← a]
assumption
example : let k := c + (a ... |
Equicontinuity.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.Algebra.UniformConvergence
import Mathlib.Topology.UniformSpace.Equicontinuity
/-!
# Algebra-related equicontinuity criterions
-/
open ... |
FactorisationProperties.lean | /-
Copyright (c) 2024 Colin Jones. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Colin Jones
-/
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.NumberTheory.Divisors
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum.Prime
... |
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.Field.IsField
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Nat.Choose.Sum
import Mathlib.LinearAlgebra.Finsupp.L... |
SDiff.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, Jeremy Avigad, Minchao Wu, Mario Carneiro
-/
import Mathlib.Data.Finset.Lattice.Lemmas
/-!
# Difference of finite sets
## Main declarations
* `Finset.instS... |
Complex.lean | /-
Copyright (c) 2025 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.Analysis.Normed.Unbundled.SpectralNorm
import Mathlib.NumberTheory.Padics.PadicNumbers
import Mathlib.Topology.Algebra.... |
LintStyle.lean | import Mathlib.Tactic.Linter.Style
import Mathlib.Order.SetNotation
/-! Tests for all the style linters. -/
/-! Tests for the `setOption` linter -/
section setOption
set_option linter.style.setOption true
-- All types of options are supported: boolean, numeric and string-valued.
-- On the top level, i.e. as commands... |
Liouville.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.CauchyIntegral
import Mathlib.Analysis.Calculus.FDeriv.Analytic
import Mathlib.Analysis.Normed.Module.Completion
/-!
# Liouville's ... |
action.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype.
From mathcomp Require Import ssrnat div seq prime fintype bigop finset.
From mathcomp... |
bigop.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
Shadow.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Alena Gusakov, Yaël Dillies
-/
import Mathlib.Data.Finset.Grade
import Mathlib.Data.Finset.Sups
import Mathlib.Logic.Function.Iterate
/-!
# Shadows
This file defines shad... |
Module.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Frédéric Dupuis
-/
import Mathlib.Algebra.Star.SelfAdjoint
import Mathlib.Algebra.Module.Basic
import Mathlib.Algebra.Module.Equiv.Defs
import Mathlib.Algebra.Module.LinearMa... |
PresheafedSpace.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Elementwise
import Mathlib.Topology.Sheaves.Presheaf
/-!
# Presheafed spaces
Introd... |
Vieta.lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang
-/
import Mathlib.Algebra.Polynomial.Splits
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
/-!
# Vieta's Formula
The main result is `Multiset.prod_X_add_C_eq_sum_... |
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.Order.Max
import Mathlib.Order.ULift
import Mathlib.Tactic.Push
import Mathlib.Tactic.Finiteness.Attr
import Mathlib.Util.AssertExists
/-!
# ⊤ and ⊥, ... |
HomologicalComplex.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.Additive
import Mathlib.CategoryTheory.Idempotents.Karoubi
/-!
# Idempotent completeness and homological complexes
This file contains simplifi... |
Finite.lean | /-
Copyright (c) 2025 Floris van Doorn and Hannah Scholz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Hannah Scholz
-/
import Mathlib.Topology.CWComplex.Classical.Basic
/-!
# Finiteness notions on CW complexes
In this file we define what it mean... |
separable.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
ZPow.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.Deriv.Pow
import Mathlib.Analysis.Calculus.Deriv.Inv
import Mathlib.Analysis.Calculus.Deriv.Shift
/-!
# Deriv... |
ENat.lean | /-
Copyright (c) 2022 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.ENat.Basic
import Mathlib.Topology.Instances.Discrete
import Mathlib.Order.Interval.Set.WithBotTop
import Mathlib.Order.Filter.Pointwise
import Mathli... |
Polynomial.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Lemmas
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.... |
Sqrt.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.Order.Ring.Abs
import Mathlib.Algebra.Order.Ring.Unbundled.Rat
import Mathlib.Data.Rat.Lemmas
import Mathlib.Data.Int.Sqrt
/-!... |
Resolution.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.QuasiIso
import Mathlib.Algebra.Homology.SingleHomology
import Mathlib.CategoryTheory.Preadditive.Projective.Preserves
/-!
# P... |
Delaborators.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.Init
import Mathlib.Util.PPOptions
import Lean.PrettyPrinter.Delaborator.Builtins
/-! # Pi type notation
Provides the `Π x : α, β x` notation as an alterna... |
UniversallyClosed.lean | /-
Copyright (c) 2023 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Etienne Marion
-/
import Mathlib.Topology.Maps.Proper.Basic
import Mathlib.Topology.Compactification.StoneCech
/-!
# A map is proper iff it is continuous and unive... |
Equiv.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import Mathlib.Topology.Algebra.Module.LinearMapPiProd
/-!
# Continuous linear... |
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... |
DershowitzManna.lean | /-
Copyright (c) 2024 Haitian Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Haitian Wang, Malvin Gattinger
-/
import Mathlib.Algebra.Order.Sub.Unbundled.Basic
import Mathlib.Data.Multiset.OrderedMonoid
/-!
# Dershowitz-Manna ordering
In this file we define the... |
Complex.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.Complex.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
/-! # Equip `ℂ` with the Borel sigma-algebra -/
noncomputable s... |
Init.lean | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Mathlib.Init
import Aesop
/-!
# Category Theory Rule Set
This module defines the `CategoryTheory` Aesop rule set which is used by the
`aesop_cat` tactic. Ae... |
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
-/
import Mathlib.Tactic.Monotonicity.Attr
import Mathlib.Tactic.SetLike
import Mathlib.Data.Set.Basic
/-!
# Typeclass for types with a set-like extensionality property
The ... |
Quotient.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Eric Wieser
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Ideal.Nonunits
import Mathlib.RingTheory.Ideal.Quotient.De... |
Basic.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.Algebra.Subalgebra.Tower
import Mathlib.Algebra.Field.IsField
import Mathlib.Algebra.Field.Subfield.Basic
import Mathlib.Algebra.Polynomial.AlgebraMa... |
countalg.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ss... |
fingroup.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 fintype div path... |
JacobiSymbol.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Thomas Zhu, Mario Carneiro
-/
import Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity
/-!
# The Jacobi Symbol
We define the Jacobi symbol and prove its main pro... |
Support.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.Algebra.Exact
import Mathlib.RingTheory.Ideal.Colon
import Mathlib.RingTheory.Localization.Finiteness
import Mathlib.RingTheory.Nakayama
import Mathlib.RingT... |
UnitTrinomial.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Polynomial.UnitTrinomial
import Mathlib.Analysis.Complex.Polynomial.Basic
/-!
# Irreducibility of unit trinomials
## TODO
Develop more the... |
Ring.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.Algebra.Order.Ring.Defs
import Mathlib.Order.Filter.AtTopBot.Group
/-!
# Convergence to ±infinity in ordered rings
-/
variable {α β : Type*}
names... |
Equalizers.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Indization.FilteredColimits
import Mathlib.CategoryTheory.Limits.FullSubcategory
import Mathlib.CategoryTheory.Limits.Indization.Pa... |
Congr.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 Fréchet derivative: congruence properties
Lemmas about congruence properti... |
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, Jeremy Avigad, Yury Kudryashov
-/
import Mathlib.Order.Filter.Ultrafilter.Defs
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.ZornAtoms
/-!
# Ultrafilters
... |
Presheaf.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.Generator.Basic
import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
/-!
# Generators in the category of presheaves
In this file, we show... |
AddTorsor.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Normed.Group.AddTorsor
import Mathlib.LinearA... |
FreeAlgebra.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.FreeAlgebra
import Mathlib.LinearAlgebra.Basis.Cardinality
import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
import Mathlib.LinearAlgebra.Di... |
Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.Notation.Lemmas
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Ring... |
GradedModule.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.RingTheory.GradedAlgebra.Basic
import Mathlib.Algebra.GradedMulAction
import Mathlib.Algebra.DirectSum.Decomposition
import Mathlib.Algebra.Module.BigOpera... |
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