filename stringlengths 5 42 | content stringlengths 15 319k |
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test_ssrAC.v | From mathcomp Require Import all_boot ssralg.
Section Tests.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite orbACA. Abort.
Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d).
Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort.
Lemma ... |
BundledFun.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.Algebra.Order.Monoid.Defs
import Mathlib.Topology.UniformSpace.Ultra.Basic
/-!
# Pseudometrics as bundled functions
This file defines a pseudometri... |
DerivativeTest.lean | /-
Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Kjos-Hanssen, Patrick Massot, Floris van Doorn, Jireh Loreaux, Eric Wieser
-/
import Mathlib.Topology.Order.OrderClosedExtr
import Mathlib.Analysis.Calculus.Deriv.MeanValue
i... |
GradedObject.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Joël Riou
-/
import Mathlib.CategoryTheory.ConcreteCategory.Basic
import Mathlib.CategoryTheory.Shift.Basic
import Mathlib.Data.Set.Subsingleton
import Mathlib.Algebra.Grou... |
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.Group.Action.Pi
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.Gro... |
Lemmas.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Indicator
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.Finset.Lattice.Fold
/-!
# Some lemmas on extended non-n... |
Mathlib.lean | import Std
import Batteries
import Mathlib.Algebra.AddConstMap.Basic
import Mathlib.Algebra.AddConstMap.Equiv
import Mathlib.Algebra.AddTorsor.Basic
import Mathlib.Algebra.AddTorsor.Defs
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algeb... |
Opposite.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.Data.Opposite
import Mathlib.Data.Set.Operations
/-!
# The opposite of a set
The opposite of a set `s` is simply the set obtained by taking the opposit... |
Shrink.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.Data.Countable.Small
import Mathlib.Data.Fintype.EquivFin
/-!
# Fintype instance for `Shrink`
-/
universe u v
variable {α : Type u} [Fintype α]
noncompu... |
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... |
sylow.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 prime bigop finset fingroup morphism.
From mat... |
Product.lean | /-
Copyright (c) 2021 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Topology.Constructions
import Mathlib.Topology.Homotopy.Path
/-!
# Product of homotopies
In this file, we introduce definitions for the produ... |
ssrint.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import fintype finfun b... |
Indicator.lean | /-
Copyright (c) 2024 PFR contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: PFR contributors
-/
import Mathlib.Algebra.Notation.Indicator
import Mathlib.Topology.Piecewise
import Mathlib.Topology.Clopen
/-!
# Continuity of indicator functions
-/
open Set
o... |
Imo1963Q5.lean | /-
Copyright (c) 2024 Rida Hamadani. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rida Hamadani
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex
/-!
# IMO 1963 Q5
Prove that `cos (π / 7) - cos (2 * π / 7) + cos (3 * π / 7) = 1 / 2`.
The main idea ... |
falgebra.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 choice fintype div... |
Init.lean | /-
Copyright (c) 2023 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
import Mathlib.Init
import Aesop
/-!
# arith_mult Rule Set
This module defines the `IsMultiplicative` Aesop rule set which is used by the
`arith_mult` tactic. ... |
Hint.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Lean.Meta.Tactic.TryThis
import Batteries.Linter.UnreachableTactic
import Batteries.Control.Nondet.Basic
/-!
# The `hint` tactic.
The `hint` tactic tries the kit... |
EpiMono.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.ObjectProperty.ClosedUnderIsomorphisms
import Mathlib.Algebra.Homology.ShortComplex.ShortExact
/-!
# Properties of objects that are closed under ... |
DeprecatedSyntaxLinter.lean | import Mathlib.Tactic.Cases
import Mathlib.Tactic.Linter.DeprecatedSyntaxLinter
set_option linter.style.refine true
/--
warning:
The `refine'` tactic is discouraged: please strongly consider using `refine` or `apply` instead.
Note: This linter can be disabled with `set_option linter.style.refine false`
---
warning:
T... |
Metric.lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Vincent Beffara, Rida Hamadani
-/
import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
import Mathlib.Data.ENat.Lattice
/-!
# Graph metric
This module defines th... |
Extensive.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.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.StrictInitial
import Mathlib.CategoryTheory.Limits.Types.Shapes
impo... |
Basic.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Algebra.Algebra.Field
import Mathlib.Algebra.BigOperators.Balance
import Mathlib.Algebra.Order.BigOperators.Expect
import Mathlib.Algebra.Order.Star.... |
Basic.lean | /-
Copyright (c) 2019 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Kim Morrison, Yuyang Zhao
-/
import Mathlib.Data.Nat.Basic
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Convert
import Mathlib.... |
SingleObj.lean | /-
Copyright (c) 2023 Antoine Labelle. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle
-/
import Mathlib.Combinatorics.Quiver.Cast
import Mathlib.Combinatorics.Quiver.Symmetric
/-!
# Single-object quiver
Single object quiver with a given arrows type.
... |
Hull.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Order.Closure
/-!
# Convex hull
This file defines the convex hull of a set `s` in a module. `con... |
WideEqualizers.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
/-!
# Wide equalizers and wide coequalizers
This file defines wide... |
ZeroCons.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Multiset.Defs
import Mathlib.Order.BoundedOrder.Basic
/-!
# Definition of `0` and `::ₘ`
This file defines constructors for multisets:
* ... |
IsCardinalFiltered.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.Filtered.Basic
import Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers
import Mathlib.CategoryTheory.Comma.CardinalArrow
import Mathlib.SetTheo... |
UnionInter.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Perm.Lattice
import Mathlib.Data.Multiset.Filter
import Mathlib.Order.MinMax
import Mathlib.Logic.Pairwise
/-!
# Distributive lattice... |
Basic.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Control.Basic
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Option.Basic
im... |
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... |
ENNRealLog.lean | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
import Mathlib.Data.EReal.Basic
/-!
# Extended Nonnegative Real... |
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... |
Count.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Nodup
import Mathlib.Data.Multiset.ZeroCons
/-!
# Counting multiplicity in a multiset
-/
-- No algebra should be required
assert_no... |
Complexity.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.ModelTheory.Equivalence
/-!
# Quantifier Complexity
This file defines quantifier complexity of first-order formulas, and constructs prenex normal for... |
AEStronglyMeasurable.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
/-!
# Strongly measurable and finitely strongly measurable functions
A function `f` is... |
Basic.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.Algebra.Module.LinearMap
/-!
# Algebraic operations on `SeparationQuotient`
In this file we define algebraic operations (multiplication, a... |
Cardinality.lean | /-
Copyright (c) 2022 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Polynomial.Cardinal
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.RingTheory.Algebraic.Defs
/-!
# Cardinality of algebraic extensions
Th... |
ArithmeticFunction.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.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Module.BigOperators
import Mathlib.NumberTheory.Divisors
import Mathlib.Data.Nat.Squarefree
imp... |
BorelCantelli.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Yury Kudryashov
-/
import Mathlib.MeasureTheory.OuterMeasure.AE
/-!
# Borel-Cantelli lemma, part 1
In this file we show one implication of the **Borel-Cantelli lemma**:... |
Comma.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
import Mathl... |
DedekindDomain.lean | /-
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin
-/
import Mathlib.Algebra.Module.Torsion
import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
/-!
# Modules over a Dedekind domain
Over a Dedekind dom... |
HasseDeriv.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Data.Nat.Choose.Cast
import Mathlib.Data.Nat.Choose.Vanderm... |
Basic.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Equivalence
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal... |
ConjAct.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GroupWithZero.Basic
import Mathlib.GroupTheory.GroupAction.ConjAct
/-!
# Conjugation action of a group with zero on itself
-/
assert_not_exists Rin... |
TakeWhile.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Mathlib.Order.Basic
import Mathlib.Data.Nat.Basic
import Mathlib.Tactic.Set
/-! ### Li... |
Unique.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.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital
import Mathlib.Topology.ContinuousMap.StoneWeierstrass
import Mathlib.Analysis.InnerProductS... |
Hom.lean | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Group.Hom.Instances
/-! # Zero-related `•` instances on group-like morphisms -/
variable {M N A B... |
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... |
Operations.lean | /-
Copyright (c) 2022 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov, Yakov Pechersky, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Prod
impor... |
ConvergentsEquiv.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.ContinuantsRecurrence
import Mathlib.Algebra.ContinuedFractions.TerminatedStable
import Mathlib.Tactic.FieldSimp
import ... |
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... |
Eval.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.Init
import Qq.Macro
/-!
# The `eval%` term elaborator
This file provides the `eval% x` term elaborator, which evaluates the constant `x` at compile-time
... |
ClearExclamation.lean | /-
Copyright (c) 2022 Joshua Clune. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joshua Clune
-/
import Mathlib.Init
import Lean.Elab.Tactic.ElabTerm
/-! # `clear!` tactic -/
namespace Mathlib.Tactic
open Lean Meta Elab.Tactic
/-- A variant of `clear` which clears... |
Simplex.lean | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Analysis.Normed.Group.AddTorsor
import Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
/-!
# Simplices in torsors over normed spaces.
This file defines p... |
order.v | (* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import path fintype tup... |
all_fingroup.v | From mathcomp Require Export action.
From mathcomp Require Export automorphism.
From mathcomp Require Export fingroup.
From mathcomp Require Export gproduct.
From mathcomp Require Export morphism.
From mathcomp Require Export perm.
From mathcomp Require Export presentation.
From mathcomp Require Export quotient.
|
FunctionField.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.NumberTheory.ClassNumber.AdmissibleCardPowDegree
import Mathlib.NumberTheory.ClassNumber.Finite
import Mathlib.NumberTheory.FunctionField
/-!
# Class number... |
Bilinear.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.Algebra.Module.Submodule.Bilinear
/-!
# Finitely generated submodules and bilinear maps
-/
open Function (... |
Module.lean | /-
Copyright (c) 2025 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
import Mathlib.RingTheory.KrullDimension.NonZeroDivisors
import Mathlib.RingTheory.Spectrum.Prime.Module
/-!
# Krull Dimension of Module
In this file we define `Module.s... |
imset2_finset.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Check @imset2_pair.
|
EnoughInjectives.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Category.Grp.EnoughInjectives
import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Ring.Shrink
/-!
# Category of $R$-mod... |
LeftHomotopy.lean | /-
Copyright (c) 2025 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.ModelCategory.Cylinder
import Mathlib.CategoryTheory.Localization.Quotient
/-!
# Left homotopies in model categories
We introduce the types `... |
Prod.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Data.Finset.Prod
/-!
# Lattice operations on finsets of products
This file is concerned with folding binary l... |
Reduced.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Scott Carnahan
-/
import Mathlib.LinearAlgebra.RootSystem.IsValuedIn
/-!
# Reduced root pairings
This file contains basic definitions and results related to reduced root pa... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
-/
import Mathlib.Data.Countable.Small
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fintype.Powerset
import Mathlib.Dat... |
Min.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.Torsion
import Mathlib.Data.ENat.Lattice
import Mathlib.Data.ZMod.QuotientGroup
/-!
# Minimum order of an element
This file defines the min... |
Embedding.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.Order.Fin.Basic
/-! # Constructions of embeddings of `Fin n` into a type
* `Fin.Embedding.cons` : f... |
Topology.lean | /-
Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.SetTheory.Ordinal.Enum
import Mathlib.Tactic.TFAE
import Mathlib.Topology.Order.Monotone
/-!
### Topology of ordinals
We prov... |
Lists.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Sigma.Basic
import Mathlib.Algebra.Order.Ring.Nat
/-!
# A computable model of ZFA without infinity
In this file we define finite hereditary list... |
PolynomialGaloisGroup.lean | /-
Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Patrick Lutz
-/
import Mathlib.FieldTheory.Galois.Basic
/-!
# Galois Groups of Polynomials
In this file, we introduce the Galois group of a polynomial... |
NNReal.lean | /-
Copyright (c) 2025 Yoh Tanimioto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
import Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real
/-!
# Riesz–Markov–Kakutani representation theorem for `ℝ≥0`
This file proves the Riesz-Markov-Kakutan... |
MetrizableSpace.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov, Aaron Liu
-/
import Mathlib.Topology.MetricSpace.HausdorffDistance
import Mathlib.Topology.Metrizable.Basic
import Mathlib.Topology.Separation.GD... |
RingHom.lean | /-
Copyright (c) 2015 Nathaniel Thomas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Action.End
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Ring.Hom.... |
ExpDecay.lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.MeasureTheory.Integral.Asymptotics
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
import Mathlib.MeasureTheory.Integral.IntegralEqImprope... |
Pretriangulated.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.HomotopyCategory.MappingCone
import Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
import Mathlib.CategoryTheory.Triangulated.Functor... |
FixedDetMatrices.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
import Mathlib.Data.Int.Interval
/-!
# Matrices with fixed determinant
This file defines the type of matrice... |
PreservesHomology.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.QuasiIso
import Mathlib.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
/-!
... |
burnside_app.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... |
ExtractGoal.lean | import Mathlib.Tactic.ExtractGoal
import Mathlib.Order.Basic
import Mathlib.Data.Nat.Basic
set_option linter.style.setOption false
set_option pp.unicode.fun true
set_option autoImplicit true
set_option linter.unusedVariables false
-- the example in the documentation for the tactic.
/-- info: theorem _example.extracte... |
IntegerCompl.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
/-!
# Integer Complement
We define the complement of the integers in the complex plane and give some basic lem... |
IsometryEquiv.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Eric Wieser
-/
import Mathlib.LinearAlgebra.QuadraticForm.Basic
import Mathlib.LinearAlgebra.QuadraticForm.Isometry
/-!
# Isometric equivalences with respect to quadratic fo... |
TotallyUnimodular.lean | /-
Copyright (c) 2024 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak, Vladimir Kolmogorov, Ivan Sergeev, Bhavik Mehta
-/
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.Data.Matrix.ColumnRowPartitioned
import Mathlib.Da... |
test_regular_conv.v | From mathcomp Require Import all_boot all_order all_algebra all_field.
Section regular.
Import GRing.
Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType.
Proof. by move=> [? []]. Qed.
Goal forall R : comRingType, [the algType R of R^o] = R :> ringType.
Proof. by move=> [? []]. Qed.
Goal forall R : c... |
NonZeroDivisors.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.RingTheory.Ideal.MinimalPrime.Localization
import Mathlib.RingTheory.KrullDimension.Basic
import Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors
import Mathl... |
RootPairingCat.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.LinearAlgebra.RootSystem.Hom
import Mathlib.CategoryTheory.Category.Basic
/-!
# The category of root pairings
This file defines the category of root p... |
ContentIdeal.lean | /-
Copyright (c) 2025 Fabrizio Barroero. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Barroero
-/
import Mathlib.Order.CompletePartialOrder
import Mathlib.RingTheory.Ideal.Quotient.Operations
import Mathlib.RingTheory.Polynomial.Content
/-!
# The content i... |
MulExpNegMulSq.lean | /-
Copyright (c) 2024 Jakob Stiefel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Stiefel
-/
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Topology.ContinuousMap.Bounded.Normed
/-!
# Definit... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Jeremy Avigad
-/
import Mathlib.Order.SetNotation
import Mathlib.Tactic.Continuity
import Mathlib.Tactic.FunProp
import Mathlib.Tactic.MkIffOfInductiveP... |
MellinTransform.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
... |
DirectSumIsInternal.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
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Algebra.Group.ConjFinite
import Mathlib.Data.Fintype.Lattice
import Mathlib.Tactic.FinCases
/-!
# Not... |
IntegralCharFun.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc
import Mathlib.MeasureTheory.Measure.CharacteristicFu... |
GabrielPopescu.lean | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Algebra.Category.ModuleCat.Injective
import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected
import Mathlib.CategoryTheory.Abelian.Grothendiec... |
Adjunctions.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johan Commelin
-/
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.CategoryTheory.Monoidal.Types.Basic
import Mathlib.LinearAlgebra.DirectSum.Finsupp... |
LocallyInjective.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.Sites.LeftExact
import Mathlib.CategoryTheory.Sites.PreservesSheafification
import Mathlib.CategoryTheory.Sites.Subsheaf
import Mathlib.CategoryTh... |
WellApproximable.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Dynamics.Ergodic.AddCircle
import Mathlib.MeasureTheory.Covering.LiminfLimsup
/-!
# Well-approximable numbers and Gallagher's ergodic theorem
Gallagher's e... |
Basic.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.Order.Group.Multiset
import Mathlib.Data.Setoid.Basic
import Mathlib.Data.Vector.Basic
import Mathlib.Logic.Nontrivial.Basic
import Mathlib.Tactic.Ap... |
Defs.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.SpecialFunctions.Pow.NNReal
import Mathlib.MeasureTheory.Function.EssSup
import Mathlib.MeasureTheory.Function.StronglyMeasurab... |
RCLike.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Analysis.Calculus.ContDiff.Defs
import Mathlib.Analysis.Calculus.MeanValue
/-!
# Higher differentiability over `ℝ` or `ℂ`
-/
... |
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