filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Encoding.lean | /-
Copyright (c) 2020 Pim Spelier, Daan van Gent. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pim Spelier, Daan van Gent
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Num.Lemmas
import Mathlib.Data.Option.Basic
import Mathlib.SetTheory.Cardinal.Basic
impo... |
classfun.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
Sort.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Sort
import Mathlib.Data.Multiset.Range
import Mathlib.Util.Qq
/-!
# Construct a sorted list from a multiset.
-/
variable {α β : Type*}
na... |
Chain.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.RootSystem.Finite.Lemmas
import Mathlib.Order.Interval.Set.OrdConnectedLinear
/-!
# Chains of roots
Given roots `α` and `β`, the `α`-chain th... |
EffectiveEpimorphic.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Sieves
import Mathlib.CategoryTheory.EffectiveEpi.Basic
/-!
# Effective epimorphic sieves
We define the notion of effective epimorphic (... |
BitVec.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Harun Khan, Alex Keizer
-/
import Mathlib.Algebra.Ring.InjSurj
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.ZMod.Defs
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Basi... |
Prod.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.CliffordAlgebra.Grading
import Mathlib.LinearAlgebra.TensorProduct.Graded.Internal
import Mathlib.LinearAlgebra.QuadraticForm.Prod
/-!
# Cliff... |
Sign.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Data.Sign.Defs
deprecated_module (since := "2025-05-11")
|
Opposites.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Thomas Read, Andrew Yang
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Yoneda
import Mathlib.CategoryTheory.Opposites
/-!
# Opposite adju... |
Range.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.Insert
import Mathlib.Data.Multiset.Range
import Mathlib.Order.Interval.Set.Defs
/-!
... |
SuccOrder.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.Order.LatticeIntervals
import Mathlib.Order.SuccPred.Basic
/-!
# Successors in intervals
If `j` is an element of a partially ordered set equipped
with a succes... |
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.
(**********************... |
ConstructibleSet.lean | /-
Copyright (c) 2024 Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Andrew Yang
-/
import Mathlib.Order.SuccPred.WithBot
import Mathlib.RingTheory.Spectrum.Prime.Topology
/-!
# Constructible sets in the prime spectrum
This fi... |
GoingUp.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Yongle Hu
-/
import Mathlib.RingTheory.Ideal.Over
import Mathlib.RingTheory.Localization.AtPrime.Basic
import Mathlib.RingTheory.Localization.Integral
/-!
# Ideals over/unde... |
Header.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Tactic.Linter.Header
import Lake
import Mathlib.Tactic.Linter.Header
import /- -/ Mathlib.Tactic -- the `TextBased` linter does not flag this `broadImpo... |
Basic.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.Algebra.CharP.Basic
import Mathlib.Algebra.CharP.Lemmas
import Mathlib.Algebra.Ring.Regular
import Mathlib.Data.Fintype.Units
import Mathlib.GroupTheory.... |
Partition.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Bryan Gin-ge Chen, Patrick Massot, Wen Yang, Johan Commelin
-/
import Mathlib.Data.Set.Finite.Range
import Mathlib.Order.Partition.Finpartition
/-!
# Equivalenc... |
DeriveFintype.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Tactic.ProxyType
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Sigma
import Mathlib.Data.Fintype.Sum
/-!
# The `Fintype` derive handler
Thi... |
ParseCommand.lean | /-
Copyright (c) 2024 Matthew Robert Ballard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matthew Robert Ballard, Damiano Testa
-/
import Lean.Elab.Command
import Mathlib.Init
/-!
# `#parse` -- a command to parse text and log outputs
-/
namespace Mathlib.GuardExc... |
Lemmas.lean | /-
Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Squarefree.Basic
import Mathlib.RingTheory.ChainOfDivisors
i... |
AffineScheme.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.AlgebraicGeometry.Cover.Open
import Mathlib.AlgebraicGeometry.GammaSpecAdjunction
import Mathlib.AlgebraicGeometry.Restrict
import Mathlib.CategoryTheory.Lim... |
Filtration.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import Mathlib.MeasureTheory.Constructions.Cylinders
import Mathlib.MeasureTheory.Function.ConditionalExpectation.Real
import Mathlib.MeasureTheory.Measurable... |
List.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.Data.Finset.Powerset
import Mathlib.Data.Fintype.Defs
import Mathlib.Data.List.Permutation
/-!
# Fintype instance for nodup lists
The subtype of `... |
Int.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Algebra.EuclideanDomain.Defs
import Mathlib.Algebra.Order.Group.Unbundled.Int
import Mathlib.Algebra.... |
Bounds.lean | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.FieldTheory.Finite.Basic
import Mathlib.NumberTheory.DirichletCharacter.Basic
/-!
# Bounds for values of Diri... |
MersennePrimes.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.NumberTheory.LucasLehmer
/-!
# Explicit Mersenne primes
We run some Lucas-Lehmer tests to prove the first Mersenne primes are prime.
See the discussion ... |
AlternatingConst.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.Algebra.Homology.ShortComplex.HomologicalComplex
import Mathlib.Algebra.Module.BigOperators
import Mathlib.AlgebraicTopology.ExtraDegeneracy
/-!
# The alter... |
Relator.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
/-!
# Relator for functions, pairs, sums, and lists.
-/
namespace Relator
universe u₁ u₂ v₁ v₂
/- TODO(johoelzl):
* should we i... |
GroupCompletion.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.Topology.Algebra.UniformMulAction
import Mathlib.Topology.UniformSpace.Completion
import Mathlib.Topology.Algebra.Group.Pointwise
/-!
... |
Slice.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.Tactic.Conv
/-!
# The `slice` tactic
Applies a tactic to an interval of terms from a term obtained by repeat... |
factors.lean | import Mathlib.Tactic.Simproc.Factors
example : Nat.primeFactorsList 0 = [] := by simp only [Nat.primeFactorsList_ofNat]
example : Nat.primeFactorsList 1 = [] := by simp only [Nat.primeFactorsList_ofNat]
example : Nat.primeFactorsList 2 = [2] := by simp only [Nat.primeFactorsList_ofNat]
example : Nat.primeFactorsList ... |
Proper.lean | /-
Copyright (c) 2024 Yaël Dillies, Kalle Kytölä, Kin Yau James Wong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Kalle Kytölä, Kin Yau James Wong
-/
import Mathlib.Probability.Kernel.Composition.CompNotation
/-!
# Proper kernels
This file defines pr... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
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... |
ReduceOption.lean | /-
Copyright (c) 2020 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky, Anthony DeRossi
-/
import Mathlib.Data.List.Basic
/-!
# Properties of `List.reduceOption`
In this file we prove basic lemmas about `List.reduceOption`.
-/
namespac... |
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, Jens Wagemaker, Yaël Dillies
-/
import Mathlib.Algebra.Group.Units.Defs
import Mathlib.Logic.Basic
/-!
# Irreducible elements in a monoid
This file defines irreducibl... |
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... |
Removal.lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.SimpleGraph.DegreeSum
import Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma
import Mathlib.Combinatorics.Simp... |
AddContent.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Peter Pfaffelhuber
-/
import Mathlib.MeasureTheory.SetSemiring
import Mathlib.MeasureTheory.OuterMeasure.Induced
/-!
# Additive Contents
An additive content `m` on a set ... |
Circle.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Analysis.Normed.Field.UnitBall
/-!
# The circle
This file defines `circle` to be the m... |
eval_elab.lean | import Mathlib.Tactic.Eval
import Mathlib.Data.Finset.Powerset
import Mathlib.Data.Finset.Sort
import Mathlib.Util.Qq
#guard_expr eval% 2^10 =ₛ 1024
#guard_expr (eval% 2^10 : Int) =ₛ (1024 : Int)
#guard_expr
(eval% Multiset.powerset ({1, 2, 3} : Multiset ℕ)) =
{0, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, ... |
hall.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 choice.
From mathcomp Require Import fintype finset prime fingroup morphism.
From ma... |
Algebra.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.Algebra.Pi
import Mathlib.Algebra.GroupWithZero.Indicator
import Mathlib.LinearAlgebra.Pi
import Mathlib.Topology.LocallyConstant.Basic
/-!
# ... |
FBinop.lean | import Mathlib.Tactic.FBinop
import Mathlib.Data.Set.Prod
import Mathlib.Data.Finset.Prod
import Mathlib.Data.SetLike.Basic
private axiom test_sorry : ∀ {α}, α
universe u v w
set_option autoImplicit true
namespace FBinopTests
/-- Notation type class for the set product `×ˢ`. -/
class SProd' (α : Type u) (β : Type v)... |
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... |
Cyclotomic105.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic
import Mathlib.Tactic.NormNum.Prime
/-!
# Not all coefficients of cyclotomic polynomials are -1, 0, or 1
We ... |
Duality.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.GroupTheory.FiniteAbelian.Duality
import Mathlib.NumberTheory.MulChar.Basic
/-!
# Duality for multiplicative characters
Let `M` be a finite commutative... |
all_ssreflect.v | Attributes deprecated(since="mathcomp 2.5.0",
note="Use 'all_boot' and/or 'all_order' instead.").
From mathcomp Require Export all_boot.
From mathcomp Require Export preorder.
From mathcomp Require Export order.
|
IntegrableExpMul.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.L1Space.Integrable
import Mathlib.MeasureTheory.Order.Group.Lattice
/-!
# Domain of the moment generating function
For `X` a real ... |
MulAntidiagonal.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Floris van Doorn
-/
import Mathlib.Order.WellFoundedSet
/-! # Multiplication antidiagonal -/
namespace Set
variable {α : Type*}
section Mul
variable [Mul α] {s s₁... |
BigOperators.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.BigOperators.Group.Finset.Piecewise
import Mathlib.Algebra.Group.Pointwise.Set.Basic
import Mathlib.Data.Fintype.Card
/-!
# Results about pointwise ... |
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 ... |
AList.lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
-/
import Mathlib.Data.List.Sigma
/-!
# Association Lists
This file defines association lists. An association list is a list where every element consists o... |
Determinant.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.Ring
/-!
# Deter... |
matrix.lean | /-
manually ported from
https://github.com/leanprover-community/mathlib/blob/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b/test/matrix.lean
-/
import Mathlib.Data.Matrix.Notation
import Mathlib.GroupTheory.Perm.Fin
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Qq
set_option linter.style.commandStart false
o... |
QuadraticReciprocity.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.NumberTheory.Zsqrtd.GaussianInt
import Mathlib.NumberTheory.LegendreSymbol.Basic
/-!
# Facts about the gaussian integers relying on quadratic reciprocity.... |
Series.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies
-/
import Mathlib.Analysis.SpecialFunctions.Exponential
import Mathlib.Data.Complex.Trigonometric
/-!
# Trigonometric functions as sums of infinite series
In t... |
generic_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice.
From mathcomp Require Import seq fintype.
(*****... |
Order.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Aaron Anderson
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.Module.Defs
import Mathlib.Algebra.Order.Pi
import Mathlib.Algebra... |
Inverse.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.Trigonometric.Basic
import Mathlib.Topology.Order.ProjIcc
/-!... |
BooleanRing.lean | /-
Copyright (c) 2021 Bryan Gin-ge Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Gin-ge Chen, Yaël Dillies
-/
import Mathlib.Algebra.Group.Idempotent
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Algebra.Ring.PUnit
import Mathlib.Order.Hom.BoundedLattic... |
Goursat.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.GroupTheory.Goursat
import Mathlib.LinearAlgebra.Prod
import Mathlib.LinearAlgebra.Quotient.Basic
/-!
# Goursat's lemma for submodules
Let `M, N` be ... |
LogMeromorphic.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.Meromorphic.FactorizedRational
import Mathlib.Analysis.NormedSpace.Connected
import Mathlib.Analysis.SpecialFunctions.Integrability.Basic
impo... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
Yoneda.lean | import Mathlib.CategoryTheory.Monoidal.Mon_
deprecated_module (since := "2025-05-11")
|
Zero.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Category.Grp.Basic
import Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
/-!
# The category of (commutative) (additive) groups has a zero object... |
Bind.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
/-!
# Bind operation for multisets
This file defines a few basic operations on `Multiset`, notably the mona... |
pgroup.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype bigop finset prime fingroup morphism.
From mat... |
ArithMult.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.NumberTheory.ArithmeticFunction
open ArithmeticFunction
variable {R : Type*} [Field R]
set_option linter.unusedVariables false
example : IsMu... |
Rename.lean | import Mathlib.Tactic.Rename
example (a : Nat) (b : Int) : Int × Nat := by
rename' a => c, b => d
exact (d, c)
example (a : Nat) (b : Int) : Int × Nat := by
rename' a => b, b => a
exact (a, b)
|
OrderClosedExtr.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
-/
import Mathlib.Topology.Order.OrderClosed
import Mathlib.Topology.Order.LocalExtr
/-!
# Local maxima from monotonicity and antitonicity
In ... |
Prime.lean | /-
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Num.ZNum
import Mathlib.Tactic.Ring
/-!
# Primality for binary natural numbers
This file defines versions of ... |
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... |
Shapiro.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.CategoryTheory.Preadditive.Projective.Resolution
import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic
import Mathlib.Representat... |
Synonym.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.Algebra.GroupWithZero.Defs
import Mathlib.Algebra.Order.Group.Synonym
/-!
# Group with zero structure on the order type synonyms
Transfer algebraic i... |
SchroederBernstein.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Set.Piecewise
import Mathlib.Order.FixedPoints
import Mathlib.Order.Zorn
/-!
# Schröder-Bernstein theorem, well-ordering of cardi... |
WellFounded.lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Data.DFinsupp.Lex
import Mathlib.Order.Antisymmetrization
import Mathlib.Order.GameAdd
import Mathlib.SetTheory.Cardinal.Order
import Mathlib.Tactic.AdaptationNo... |
qpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg.
From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix.
From mathcomp Require Import mxalgebra mxpoly... |
Finset.lean | /-
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Finset.Max
import Mathlib.Data.Set.Finite.Lattice
import Mathlib.Order.ConditionallyCompleteLattice.Indexed
/-!
# Conditionally complete la... |
Order.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Sigma.Lex
import Mathlib.Util.Notation3
import Mathlib.Data.Sigma.Basic
import Mathlib.Order.Lattice
import Mathlib.Order.BoundedOrder.Basic
/-!
# Or... |
Comp.lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Yuyang Zhao
-/
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Comp
import Mathlib.Analysis.Calcu... |
finfun.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple.
... |
Groebner.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.Data.Finsupp.Lex
import Mathlib.Data.Finsupp.MonomialOrder
import Mathlib.Data.Finsupp.WellFounded
import Mathlib.Data.List.TFAE
import M... |
NhdsKer.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Yury Kudryashov
-/
import Mathlib.Topology.NhdsSet
import Mathlib.Topology.Inseparable
/-!
# Neighborhoods kernel of a set
In `Mathlib/Topology/Defs/Filter.lean`, `nhdsKe... |
CommMon_.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# The category of commutative monoids in a braided monoidal category... |
OrderClosed.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, Yury Kudryashov
-/
import Mathlib.Topology.Order.LeftRight
import Mathlib.Topology.Separation.Hausdorff
/-!
# Order-closed topologies
In this file we ... |
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... |
AbelianImages.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.Abelian.Images
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels
/-!
# Preservation of coimage-image comparisons
If a functo... |
Ring.lean | /-
Copyright (c) 2021 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.GroupWithZero.Canonical
import Mathlib.Algebra.Order.Nonneg.Basic
import Mathlib.Algebra.Order.Nonneg.Lattice
import Mathlib.Algebra.... |
Basic.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Hull
import Mathlib.LinearAlgebra.AffineSpace.Independent
/-!
# Simplicial complexes
In this file, we define ... |
Real.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Topology.MetricSpace.Bounded
import Mathlib.Topology.Order.Bornology
/-!
# The reals are equipped with their order bornology
This fil... |
Rify.lean | /-
Copyright (c) 2023 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Mario Carneiro, Robert Y. Lewis, Patrick Massot
-/
import Mathlib.Data.Rat.Cast.Order
import Mathlib.Data.Real.Basic
import Mathlib.Tactic.Qify
/-!
# `rify` tactic
The `... |
Tauto.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, David Renshaw
-/
import Mathlib.Tactic.Tauto
import Mathlib.Tactic.SplitIfs
import Mathlib.Data.Part
set_option autoImplicit true
section tauto₀
variable (p q r : Prop)
var... |
poly.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 bigop fi... |
Yoneda.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.CategoryTheory.Limits.Preserves.Finite
import Mathlib.CategoryTheory.Limits.Opposites
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Product... |
Pi.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.Algebra.Notation.Pi.Basic
import Mathlib.Data.Set.BooleanAlgebra
import Mathlib.Data.Set.Piecewise
import Mathlib.Order.Interval.Set.Basic
import Mat... |
Result.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 Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Invertible
import Mathlib.Data.Sigma.Basic
import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.... |
Finite.lean | /-
Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot
-/
-- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl.
import Mathlib.Algebra.Group.Subgroup.Finite
imp... |
DenseEmbedding.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.Topology.Bases
import Mathlib.Topology.Separation.Regular
/-!
# Dense embeddings
This file defines three properties of f... |
Connected.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.Filtered.Basic
import Mathlib.CategoryTheory.IsConnected
/-!
# Filtered categories are connected
-/
universe v u
namespace CategoryTheo... |
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