filename stringlengths 5 42 | content stringlengths 15 319k |
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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... |
ApproximateUnit.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.Order
import Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart
import Mathlib.Analysis.SpecialFun... |
CartesianClosed.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.Closed.Ideal
import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory
import Mathlib.CategoryTheory.Sites.CartesianMonoidal
... |
Bitwise.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Alex Keizer
-/
import Mathlib.Algebra.Group.Nat.Even
import Mathlib.Algebra.NeZero
import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.Bool.Basic
import Mathlib.Data.List... |
Refinements.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.Abelian.Refinements
import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
/-!
# Refinements
This file contains lemmas about "refineme... |
UniqueSums.lean | /-
Copyright (c) 2025 Yaël Dillies, Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Paul Lezeau
-/
import Mathlib.Algebra.FreeAbelianGroup.Finsupp
import Mathlib.Algebra.Group.UniqueProds.Basic
/-!
# Free abelian groups have unique sums
-/
a... |
LocPathConnected.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Ben Eltschig
-/
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Topology.AlexandrovDiscrete
/-!
# Locally path-connected spaces
This file defines `LocP... |
Zify.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Mario Carneiro, Robert Y. Lewis
-/
import Mathlib.Tactic.Basic
import Mathlib.Tactic.Attr.Register
import Mathlib.Data.Int.Cast.Basic
import Mathlib.Order.Basic
/-!
# `zify`... |
Lemmas.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Probability.Kernel.Composition.MeasureComp
import Mathlib.Probability.Kernel.Composition.ParallelComp
/-!
# Lemmas relating different wa... |
Isometric.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.Instances
/-! # Isometric continuous functional calculus
This file adds a class for an *isometric* c... |
Nonempty.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.Logic.Function.Defs
/-!
# Nonempty types
This file proves a few extra facts about `Nonempty`, which is defined in core Lean.
## Main declarations
*... |
Connected.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Reid Barton, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Creates
import Mathlib.CategoryTheory.Comma.Over.Basic
import Mathlib.CategoryTheory.IsConnected
/-!
... |
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.
|
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... |
Span.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.Data.Finset.Sort
import Mathlib.Topology.Category.Profinite.CofilteredLimit
import Mathlib.Topology.Category.Profinite.Nobeling.Basic
/-!
# The go... |
ComplexShape.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Relation
import Mathlib.Logic.Function.Basic
/-!
# Shapes of homological complexes
We define a st... |
Pi.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.Unramified.Basic
/-!
# Formal-unramification of finite products of rings
## Main result
- `Algebra.FormallyUnramified.pi_iff`: If `I` is finit... |
Defs.lean | /-
Copyright (c) 2018 Johannes Hölzl. 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
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Al... |
PImage.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Finset.Option
import Mathlib.Data.PFun
import Mathlib.Data.Part
/-!
# Image of a `Finset α` under a partially defined function
In this file we... |
Zip.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Data.Vector.Basic
/-!
# The `zipWith` operation on vectors.
-/
namespace List
namespace Vector
section ZipWith
variable {α β γ : Type*} {n : ℕ} (f : α... |
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.
|
Slope.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.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Tactic.FieldSimp
/-!
# Slope of a function
In this file we define the slope of a function `f : k... |
NFA.lean | /-
Copyright (c) 2020 Fox Thomson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fox Thomson, Maja Kądziołka
-/
import Mathlib.Computability.DFA
import Mathlib.Data.Fintype.Powerset
/-!
# Nondeterministic Finite Automata
A Nondeterministic Finite Automaton (NFA) is ... |
Rat.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Hom
import Mathlib.Algebra.Algebra.Rat
/-!
# Homomorphisms of `ℚ`-algebras
-/
namespace RingHom
variable {R S : Type*}
/--... |
Basic.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.CategoryTheory.Category.Grpd
import Mathlib.CategoryTheory.Groupoid
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Homotopy.Path
i... |
Embeddings.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Xavier Roblot
-/
import Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
deprecated_mo... |
Kernel.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Probability.ConditionalProbability
import Mathlib.Probability.Kernel.Basic
import Mathlib.Probability.Kernel.Composition.MeasureComp
import Mathlib.Tactic.... |
Submonoid.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.Submonoid.Defs
import Mathlib.Algebra.Order.Monoid.Basic
import Mathlib.Order.Interval.Set.Defs
/-!
# Ordered instances on submonoids
-/
... |
Module.lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import Mathlib.Algebra.Algebra.RestrictScalars
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Data.... |
UInt.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Init
import Mathlib.Algebra.Ring.InjSurj
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.BitVec
/-!
# Adds Mathlib specific instances to the `UIntX... |
polyXY.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype tuple fi... |
Dimension.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.Ext.EnoughProjectives
/-!
# Projective dimension
In an abelian category `C`, we shall say that `X : C` has projective dimensio... |
LinearCombination.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Module.Submodule.Equiv
import Mathlib.Data.Finsupp.Option
import Mathlib.LinearAlgebra.Finsupp.Supported
/-!
# `Finsupp.linearCombination`
##... |
Nat.lean | /-
Copyright (c) 2024 Pim Otte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Otte
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Lemmas
import Mathlib.Data.Set.Finite.Lattice
import Mathlib.SetTheory.Cardinal.Finite
/-!
# Big operators on a finset in the na... |
CartanMatrix.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.Matrix.BilinearForm
import Mathlib.LinearAlgebra.RootSystem.Base
import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas
import Mathlib.LinearAlg... |
Count.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.MeasureTheory.Measure.Dirac
import Mathlib.Topology.Algebra.InfiniteSum.ENNReal
/-!
# Counting measure
In this file we define the counting measure `M... |
Basic.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, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Associated
import Mathlib.Algebra.Ring.Parity
import Mathlib.Data.Nat.Prime.Defs
/-!
# ... |
finfield.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype div tupl... |
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... |
Completion.lean | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Asymptotics.Theta
import Mathlib.Analysis.Normed.Group.Completion
/-!
# Asymptotics in the completion of a normed space
In this file we pr... |
all.v | From mathcomp Require Export all_boot.
From mathcomp Require Export all_order.
From mathcomp Require Export all_fingroup.
From mathcomp Require Export all_algebra.
From mathcomp Require Export all_solvable.
From mathcomp Require Export all_field.
From mathcomp Require Export all_character.
|
FinMeasAdditive.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.SimpleFuncDenseLp
/-!
# Additivity on measurable sets with finite measure
Let `... |
Lax.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.Functor.Prelax
import Mathlib.Tactic.CategoryTheory.Slice
import Mathlib.Tactic.CategoryTheory.ToApp
/-!
# Lax functors
A lax fu... |
Multiplicative.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors
/-!
# Multiplicative maps on unique factorization domains
## M... |
BigOperators.lean | /-
Copyright (c) 2017 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Balance
import Mathlib.Data.Complex.Basic
/-!
# Finite sums and products of complex numbers
-/
open Fintype
open s... |
StandardSmooth.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jung Tao Cheng, Christian Merten, Andrew Yang
-/
import Mathlib.Algebra.MvPolynomial.PDeriv
import Mathlib.LinearAlgebra.Determinant
import Mathlib.RingTheory.Extension.Presentation.... |
random.lean | import Mathlib.Control.Random
import Mathlib.Tactic.NormNum
import Batteries.Lean.LawfulMonad
open Random
-- TODO(kmill): remove once the mathlib ToExpr Int instance is removed
set_option eval.pp false
section Rand
/--
info: 33
-/
#guard_msgs in
#eval do
IO.runRandWith 257 (show Rand _ from do
let i ← randBou... |
Well.lean | /-
Copyright (c) 2022 Yaël Dillies, Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Junyan Xu
-/
import Mathlib.Data.Prod.Lex
import Mathlib.SetTheory.Ordinal.Rank
/-!
# Extend a well-founded order to a well-order
This file constructs a well-o... |
ModEq.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.Nat.ModEq
/-!
# Congruences modulo an integer
This file defines the equivalence relation `a ≡ b [ZMOD n]` on the integers, similarly to how
`Data.N... |
Basic.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.Analysis.SpecialFunctions.ImproperIntegrals
import Mathlib.MeasureTheory.Integral.ExpDecay
/-!
# The Gamma function
This file defines the `Γ` functio... |
TypeTags.lean | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Order.SuccPred.Archimedean
import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags
/-!
# Successor and predecessor on type tags
This file declates s... |
ModN.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.Algebra.EuclideanDomain.Int
import Mathlib.Algebra.Module.ZMod
import Mathlib.LinearAlgebra.Dimension.Free
/-!
# Quotienting out a free `ℤ`-module
If `G`... |
Basic.lean | /-
Copyright (c) 2025 Dexin Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dexin Zhang
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.ModelTheory.Semantics
/-!
# Presburger arithmetic
This file defines the first-order language of Presburger arithmetic as... |
CondVar.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.MeasureTheory.Function.ConditionalExpectation.Real
import Mathlib.MeasureTheory.Integral.Average
import Mathlib.Probability.Moments.Variance
/-!
# Conditi... |
DeltaGenerated.lean | /-
Copyright (c) 2024 Ben Eltschig. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ben Eltschig
-/
import Mathlib.CategoryTheory.Monad.Limits
import Mathlib.Topology.Category.TopCat.Limits.Basic
import Mathlib.Topology.Compactness.DeltaGeneratedSpace
/-!
# Delta-gener... |
Units.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.Group.Equiv.Defs
import Mathlib.Algebra.Group.Pi.Basic
import Mathlib.Algebra.Group.Units.Defs
import Mathlib.Util.Delaborators
/-! # Units in pi ty... |
Preserves.lean | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Preadditive.Injective.Basic
/-!
# Preservation of injective objects
We define a typeclass `Functor.PreservesInjectiveObjects`.
We resta... |
Monoidal.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Category.CoalgCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.CategoryTheory.Monoidal.Transport
import... |
Skeletal.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Category.Preorder
import Mathlib.CategoryTheory.IsomorphismClasses
import Mathlib.CategoryThe... |
SmoothSection.lean | /-
Copyright (c) 2023 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Floris van Doorn, Michael Rothgang
-/
import Mathlib.Geometry.Manifold.Algebra.LieGroup
import Mathlib.Geometry.Manifold.MFDeriv.Basic
import Mathlib.Topology.Continu... |
Norm.lean | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.Analysis.Calculus.Deriv.Abs
import Mathlib.Analysis.Calculus.LineDeriv.Basic
/-!
# Differentiability of the norm in a real normed vector space
This f... |
LiftingProperties.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.Preadditive.Injective.Basic
import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty
/-!
# Characterization of injective objects in terms o... |
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 ... |
Powerset.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.List.Sublists
import Mathlib.Data.List.Zip
import Mathlib.Data.Multiset.Bind
import Mathlib.Data.Multiset.Range
/-!
# The powerset of a multiset
... |
IsNonarchimedean.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, Fabrizio Barroero
-/
import Mathlib.Algebra.Order.Hom.Basic
import Mathlib.Data.Nat.Choose.Sum
/-!
# Nonarchimedean functions
A functi... |
CatCommSq.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.Equivalence
/-!
# 2-commutative squares of functors
Similarly as `CommSq.lean` defines the notion of commutative squares,
this file introduces t... |
IndicatorConstPointwise.lean | /-
Copyright (c) 2023 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.Algebra.Notation.Indicator
import Mathlib.Topology.Separation.Basic
/-!
# Pointwise convergence of indicator functions
In this file, we prove the equival... |
AsType.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.FinCategory.Basic
import Mathlib.Data.Fintype.EquivFin
/-!
# Finite categories are equivalent to category in `Type 0`.
-/
universe w v u
... |
Basic.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, Yongle Hu, Jingting Wang
-/
import Mathlib.FieldTheory.Fixed
import Mathlib.FieldTheory.Normal.Closure
import Mathlib.FieldTheory.Primitiv... |
AllAny.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 Batteries.Tactic.Alias
import Mathlib.Tactic.TypeStar
/-!
# Boolean quantifiers
This proves a few properties about `List.all` and `List.any`, which are the `... |
Path.lean | /-
Copyright (c) 2021 Shing Tak Lam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam
-/
import Mathlib.Topology.Homotopy.Basic
import Mathlib.Topology.Connected.PathConnected
import Mathlib.Analysis.Convex.Basic
/-!
# Homotopy between paths
In this file,... |
Sum.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Patrick Stevens
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.BigOperators.Ring.Finset
import ... |
Conv.lean | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Comon_
/-!
# The convolution monoid.
When `M : Comon_ C` and `N : Mon_ C`, the morphisms `M.X ⟶ N.X` form a monoid (in Type).
-/
... |
Finiteness.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Colimit.Module
import Mathlib.RingTheory.Finiteness.Basic
/-!
# Modules as direct limits of finitely generated submodules
We show that every module is ... |
ssrnum.v | From mathcomp Require Export orderedzmod.
From mathcomp Require Export numdomain.
From mathcomp Require Export numfield.
Module Num.
Export orderedzmod.Num.
Export numdomain.Num.
Export numfield.Num.
Module Theory.
Export orderedzmod.Num.Theory.
Export numdomain.Num.Theory.
Export numfield.Num.Theory.
End Theory.
Mo... |
Kleisli.lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Monad.Basic
/-! # Kleisli category on a (co)monad
This file defines... |
polydiv.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ssralg poly.
(**********************... |
Conv.lean | /-
Copyright (c) 2023 Robin Böhne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Böhne, Wojciech Nawrocki, Patrick Massot
-/
import Mathlib.Tactic.Widget.SelectPanelUtils
import Mathlib.Data.String.Defs
import Batteries.Tactic.Lint
import Batteries.Lean.Position... |
ContinuousMap.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.Classes
import Mathlib.Topology.ContinuousMap.Compact
import Mathlib.Topology.ContinuousMap.ZeroAtInfty
/-! # C⋆-algebras of conti... |
nilpotent.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 path.
From mathcomp Require Import fintype div bigop prime finset fingroup morphism.
Fro... |
WidePullbacks.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.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Thin
/-!
# Wide pullbacks
We define the category `WidePullbackShape`, (re... |
Conformal.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import Mathlib.Analysis.Calculus.Conformal.NormedSpace
import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic
/-!
# Angles and conformal maps
This file proves that co... |
Differentiable.lean | /-
Copyright (c) 2024 Tomáš Skřivan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tomáš Skřivan
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Comp
import Mathlib.Analysis.Calculus.FDeriv.Prod
import Mathlib.Analysis.Calculus... |
Applicative.lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Control.Functor
import Mathlib.Control.Basic
/-!
# `applicative` instances
This file provides `Applicative` instances for... |
path.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(******************************************************************************)
(* ... |
OfSequence.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.Category.Preorder
import Mathlib.CategoryTheory.EqToHom
/-!
# Functors from the category of the ordered set `ℕ`
In this file, we provide a const... |
Prod.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Measure.Prod
import Mathlib.Probability.Kernel.Composition.CompProd
import Mathlib.Probability.Kernel.Composition.CompMap
/-!
# Product and ... |
Adjunctions.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl
-/
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.GroupTheory.FreeAbelianGroup
import Mathlib.CategoryTheory.Limits.Types.Shapes
/-!
# Adjun... |
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... |
NormNum.lean | /-
Copyright (c) 2025. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: euprunin
-/
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Tactic.NormNum.OfScientific
import Mathlib.Tactic.NormNum.Eq
import Mathlib.Tactic.NormNum.Ineq
import Mathlib.Tactic.NormNum.Pow
impor... |
SplitSimplicialObject.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.AlgebraicTopology.SimplicialObject.Split
import Mathlib.AlgebraicTopology.DoldKan.Degeneracies
import Mathlib.AlgebraicTopology.DoldKan.FunctorN
/-!
# Split si... |
Basic.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.NumberTheory.GaussSum
import Mathlib.NumberTheory.MulChar.Lemmas
import Mathlib.RingTheory.RootsOfUnity.Lemmas
/-!
# Jacobi Sums
This file defines the ... |
AmpleSet.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Floris van Doorn
-/
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Analysis.Normed.Module.Convex
import Mathlib.Analysis.NormedSpace.Connected
import Mathli... |
Typeclasses.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.MeasureTheory.Measure.Typeclasses.Finite
import Mathlib.MeasureTheory.Measure.Typeclasses.NoAtoms
import Mathlib.MeasureTheory.Measure.... |
IsCofibrant.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.Instances
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Fibrant and cofibrant objects in a model category
Once a c... |
ClusterPt.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.Topology.Neighborhoods
/-!
# Lemmas on cluster and accumulation points
In this file we prove various lemmas on [cluste... |
Instances.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Batteries.Data.DList.Lemmas
import Mathlib.Control.Traversable.Equiv
import Mathlib.Control.Traversable.Instances
/-!
# Traversable instance for DLists
This file p... |
Completion.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.Analysis.Normed.Group.Uniform
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.MetricSpace.Completion
/-!
# Completion of a nor... |
Subadditive.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Order.Filter.AtTopBot.Archimedean
import Mathlib.Order.Filter.AtTopBot.Finite
import Mathlib.Order.Filter.AtTopBot.Prod
import Mathlib.Topology.A... |
Holor.lean | /-
Copyright (c) 2018 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Data.Nat.Find
import Mathlib.Algebra.Module.Pi
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Basic properties of holors
Holors... |
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