filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
alt.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 tupl... |
mxabelem.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... |
Binomial.lean | /-
Copyright (c) 2023 Scott Carnahan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Carnahan
-/
import Mathlib.Algebra.Group.Torsion
import Mathlib.Algebra.Polynomial.Smeval
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.Data.NNRat.Order
import Mathlib.Gro... |
Arctan.lean | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
/-!
# Complex arctangent
This file defines the complex arctangent `Complex.arctan` as
$$\arctan z = -\frac i2 \lo... |
Functions.lean | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Data.Finsupp.ToDFinsupp
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Int.Range
import Mathlib.Data.List.Sigma
import Plausible.Functions
/-!
#... |
Index.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.Ring.GeomSum
import Mathlib.Data.Finsupp.Fintype
import Mathlib.GroupTheory.Index
import Mathlib.LinearAlgebra.DirectSum.Finsupp
import Mathlib.Linea... |
Scalar.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, Yaël Dillies
-/
import Mathlib.Algebra.Group.Pointwise.Set.Basic
import Mathlib.Algebra.Opposites
import Mathlib.Algebra.Notation.Pi.Defs
import Mathl... |
LocallySmall.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.Localization.HasLocalization
import Mathlib.CategoryTheory.EssentiallySmall
/-!
# Locally small localizations
In this file, given `W : Morphism... |
ZeroMorphisms.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.Algebra.Notation.Pi.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryTh... |
algebraics_fundamentals.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 ssrnat eqtype seq choice.
From mathcomp Require Import div fintype path... |
ConcreteColorings.lean | /-
Copyright (c) 2023 Iván Renison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Iván Renison
-/
import Mathlib.Combinatorics.SimpleGraph.Circulant
import Mathlib.Combinatorics.SimpleGraph.Coloring
import Mathlib.Combinatorics.SimpleGraph.Hasse
import Mathlib.Data.Fi... |
ContinuousMapDense.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.MeasureTheory.Measure.Regular
import Mathlib.MeasureTheory.Function.SimpleFuncDenseLp
import Mathlib.Topology.UrysohnsLemma
import Mathlib.MeasureThe... |
TFAE.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/
import Batteries.Data.List.Lemmas
import Mathlib.Tactic.TypeStar
/-!
# The Following Are Equivalent
This file allows to state that all propositions in ... |
Opposite.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Opposites
import Mathlib.GroupTheory.Congruence.Defs
/-!
# Congruences on the opposite of a group
This file defines the order isomorph... |
Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Powerset
import Mathlib.Algebra.NoZeroSMulDivisors.Pi
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Finty... |
jordanholder.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 big... |
archimedean.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 or... |
Teichmuller.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.WittVector.Basic
/-!
# Teichmüller lifts
This file defines `WittVector.teichmuller`, a monoid hom `R →* 𝕎 R`, which embeds `r : R` as the... |
Basic.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
import Mathlib.Algebra.Order.ZeroLEOne
import Mathlib.Data.Nat.Cast.Basic
import Mathlib.Data.Nat.Cast.NeZero
impo... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
Transvection.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.Data.Matrix.Basis
import Mathlib.Data.Matrix.DMatrix
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.Re... |
Concrete.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.Group.Action.End
import Mathlib.Algebra.Group.Action.Pi
import Mathlib.CategoryTheory.Action.Basic
import Mathlib.CategoryTheory.FintypeCat
import ... |
BigOperators.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.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Rat
import Mathlib.Data.NNRat.Defs
/-! # Casting lemm... |
Basic.lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import Mathlib.Data.Int.DivMod
import Mathlib.Logic.Equiv.Set
import Mathlib.Tactic.Common
/-!
# The finite type with `n` elements
`Fin n` is the typ... |
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... |
OfFunction.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.OuterMeasure.Operations
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Outer measures from functions
Given an arbit... |
IsDiag.lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import Mathlib.LinearAlgebra.Matrix.Symmetric
import Mathlib.LinearAlgebra.Matrix.Orthogonal
import Mathlib.Data.Matrix.Kronecker
/-!
# Diagonal matrices
This file co... |
Basic.lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import Mathlib.Data.Fin.Embedding
import Mathlib.Data.Fin.Rev
import Mathlib.Order.Hom.Basic
/-!
# `Fin n` forms a bounded linear order
This file con... |
Copy.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Yaël Dillies
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Tooling to make copies of lattice structures
Sometimes it is useful to make a copy of a ... |
Adjunction.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.CategoryTheory.LiftingProperties.Basic
import Mathlib.CategoryTheory.Adjunction.Basic
/-!
# Lifting properties and adjunction
In this file, we obtain `Adjunct... |
output.v | From mathcomp Require Import
all_boot
all_order
all_algebra
all_field
all_character
all_fingroup
all_solvable.
Open Scope group_scope.
Check @cyclic_pgroup_Aut_structure.
|
Chain.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Order.Preorder.Chain
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module (since := "2025-04-13")
|
ChebyshevMarkov.lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.MeasureTheory.Function.LpSeminorm.Basic
/-!
# Chebyshev-Markov inequality in terms of Lp seminorms
In this file we formulate several versions of the Chebys... |
ssrnotations.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
(******************************************************************************)
(* - Reserved notation for various arithmetic and algebraic operations: ... |
Pasting.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
/-!
# Pasting lemma
This file proves the pasting lemma for pullbacks. That is, given the f... |
Conjneg.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.Order.Pi
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Algebra.Star.Conjneg
/-!
# Order properties of conjugation-negation
-/
open scope... |
LocalSubring.lean | /-
Copyright (c) 2024 Andrew Yang, Yaël Dillies, Javier López-Contreras. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yaël Dillies, Javier López-Contreras
-/
import Mathlib.RingTheory.Ideal.GoingUp
import Mathlib.RingTheory.LocalRing.LocalSubring
import ... |
CardEmbedding.lean | /-
Copyright (c) 2021 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Set.Finite.Range
import Mathlib.Logic.Equiv.Embedding
/-!
# Numb... |
Basic.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Divisibility.Hom
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.Group.Nat.Hom
import Mathlib.Algebra.Ring.Hom.Defs
import Mathlib.Alg... |
Card.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.Group.Action.Basic
import Mathlib.Algebra.Group.Pointwise.Set.Finite
import Mathlib.Data.Set.Card
/-!
# Cardinalities of pointwise operations on s... |
Monoidal.lean | /-
Copyright (c) 2025 Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang
-/
import Mathlib.Algebra.Category.CommAlgCat.Basic
import Mathlib.CategoryTheo... |
finmodule.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... |
Average.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
/-!
# Integral average of a function
In this file we define `MeasureTheory.average... |
AdmissibleAbs.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.Algebra.Algebra.Basic
import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
import Mathlib.Data.Real.Archimedean
/-!
# Admissible absolute value o... |
mxrepresentation.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... |
Star.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Frédéric Dupuis
-/
import Mathlib.Algebra.Star.Module
import Mathlib.Topology.Algebra.Module.Equiv
import Mathlib.Topology.Algebra.Star
/-!
# The star operation, bundled as ... |
Lemmas.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Order.Sub.Unbundled.Basic
import Mathlib.Data.Set.Lattice
import Mathli... |
Synonym.lean | /-
Copyright (c) 2020 Johan Commelin, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Damiano Testa, Yaël Dillies
-/
import Mathlib.Logic.Equiv.Defs
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.Order.Basic
/-!
# Type synonyms
This... |
Attr.lean | /-
Copyright (c) 2024 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Aesop
import Mathlib.Init
/-! # Finiteness tactic attribute -/
declare_aesop_rule_sets [finiteness]
|
Finiteness.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Algebra.Module.LocalizedModule.Int
import Mathlib.RingTheory.Localization.Algebra
import Mathlib.RingTheory.RingHom.Finite
/-!
# Finiteness prope... |
Instances.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Control.Bitraversable.Lemmas
import Mathlib.Control.Traversable.Lemmas
/-!
# Bitraversable instances
This file provides `Bitraversable` instances for concr... |
Pairwise.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.Category.Preorder
import Mathlib.CategoryTheory.Limits.IsLimit
import Mathlib.Order.CompleteLattice.Basic
/-!
# The category of "pairwise i... |
DirectSum.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.Module.Presentation.Basic
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Data.Finsupp.ToDFinsupp
/-!
# Presentation of a direct sum
If `M : ι →... |
FreeAndStrongRankCondition.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathlib.LinearAlgebra.Dimension.Subsingleton
/-!
# Some results on free modules over rings satisfying strong rank condit... |
SimpRw.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Mario Carneiro, Alex J. Best
-/
import Mathlib.Init
/-!
# The `simp_rw` tactic
This file defines the `simp_rw` tactic: it functions as a mix of `simp` and `rw`.
Like `rw`,... |
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... |
Norm.lean | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.RingTheory.FractionalIdeal.Basic
import Mathlib.RingTheory.Ideal.Norm.AbsNorm
import Mathlib.RingTheory.Localization.NormTrace
/-!
# Fractional ideal n... |
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... |
Pullbacks.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Kim Morrison, Mario Carneiro, Andrew Yang
-/
import Mathlib.Topology.Category.TopCat.Limits.Products
/-!
# Pullbacks and pushouts in the category of topological spaces
-... |
WithAbs.lean | /-
Copyright (c) 2024 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
import Mathlib.Analysis.Normed.Module.Completion
import Mathlib.Analysis.Normed.Ring.WithAbs
/-!
# WithAbs for fields
This extends the `WithAbs` mechanism to ... |
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.
... |
Basic.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.RingTheory.Ideal.GoingUp
import Mathlib.RingTheory.Polynomial.RationalRoot
/-!
# Dedekind rings and domains
This f... |
Quasispectrum.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.Algebra.Algebra.Spectrum.Basic
import Mathlib.Algebra.Algebra.Tower
import Mathlib.Algebra.Algebra.Unitization
/-!
# Quasiregularity and quasispectrum
... |
Constructor.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Newell Jensen
-/
import Mathlib.Init
import Lean.Elab.SyntheticMVars
import Lean.Meta.Tactic.Constructor
/-!
# The `fconstructor` and `econstructor` tactics
The `fconstru... |
Deriv.lean | import Mathlib
/-! Test that `simp` can prove some lemmas about derivatives. -/
open Real
example (x : ℝ) : deriv (fun x => cos x + 2 * sin x) x = -sin x + 2 * cos x := by
simp
example (x : ℝ) :
deriv (fun x ↦ cos (sin x) * exp x) x = (cos (sin x) - sin (sin x) * cos x) * exp x := by
simp; ring
/- for more... |
FiniteType.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.Morphisms.RingHomProperties
import Mathlib.RingTheory.RingHom.FiniteType
import Mathlib.RingTheory.Spectrum.Prime.Jacobson
/-!
# Morphisms... |
ScaleRoots.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Devon Tuma
-/
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.RingTheory.Coprime.Basic
import Mathlib.Tactic.... |
UniformLimitsDeriv.lean | /-
Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin H. Wilson
-/
import Mathlib.Analysis.Calculus.MeanValue
import Mathlib.Analysis.NormedSpace.RCLike
import Mathlib.Order.Filter.Curry
/-!
# Swapping limits and derivatives via u... |
all_field.v | From mathcomp Require Export algC.
From mathcomp Require Export algebraics_fundamentals.
From mathcomp Require Export algnum.
From mathcomp Require Export closed_field.
From mathcomp Require Export cyclotomic.
From mathcomp Require Export falgebra.
From mathcomp Require Export fieldext.
From mathcomp Require Export fin... |
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... |
integral_char.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... |
Replace.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Mario Carneiro
-/
import Mathlib.Tactic.Have
/-!
# Extending `replace`
This file extends the `replace` tactic from `Batteries` to allow the addition of hypotheses to
... |
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.
(*****... |
Basic.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.Topology.UniformSpace.Defs
import Mathlib.Topology.Bases
/-!
# Ultrametric (nonarchimedean) uniform spaces
Ultrametric (nonarchimedean) uniform spa... |
FaithfullyFlat.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Joël Riou
-/
import Mathlib.RingTheory.RingHom.Flat
/-!
# Faithfully flat ring maps
A ring map `f : R →+* S` is faithfully flat if `S` is faithfully flat as an `R... |
Pseudofunctor.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.CategoryTheory.Bicategory.Functor.LocallyDiscrete
import Mathl... |
TransfiniteComposition.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Limits.Connected
import Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape
import Mathlib.CategoryTheory.MorphismProperty... |
Infinite.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.CharZero.Defs
import Mathlib.Data.Fintype.EquivFin
/-! # A characteristic-zero semiring is infinite -/
open Set
variable (M : Type*) [AddMo... |
prime.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 path.
From mathcomp Require Import choice fintype div bigop.
(*************************... |
LocallySurjective.lean | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.Sites.Subsheaf
import Mathlib.CategoryTheory.Sites.CompatibleSheafification
import Mathlib.CategoryTheory.Sites.LocallyInjective
/-... |
EqToHom.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Kim Morrison
-/
import Mathlib.CategoryTheory.Opposites
/-!
# Morphisms from equations between objects.
When working categorically, sometimes one encounters an equation `h ... |
Basic.lean | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.Data.ENNReal.Operations
/-!
# The extended real numbers
This file defines `EReal`, `ℝ` with a top element `⊤` and a bottom element `⊥`, implemented as
... |
monoid.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun.
(******************************************************************************)
(* Group-like structures ... |
Lattice.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.Data.Set.Lattice
import Mathlib.Data.Set.Pairwise.Basic
/-!
# Relations holding pairwise
In this file we prove many facts about `Pairwise` and the se... |
Directed.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Algebra.Subalgebra.Lattice
import Mathlib.Data.Set.UnionLift
/-!
# Subalgebras and directed Unions of sets
## Main results
* `Subalgebra.coe_iSup_... |
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... |
Even.lean | /-
Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.Group.Nat.Defs
import Ma... |
Irrational.lean | /-
Copyright (c) 2025 Vasilii Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasilii Nesterov
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Data.Real.Irrational
import Mathlib.Tactic.NormNum.GCD
import Mathlib.Tactic.Rify
/-! # `norm_nu... |
Find.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, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Nat.Basic
import Batteries.WF
/-!
# `Nat.find` and `Nat.findGreatest`
-/
variable {m n k : ℕ} {p q : ... |
Basic.lean | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
import Mathlib.NumberTheory.EllipticDivisibilitySequence
/-!
# Division polynomials o... |
Defs.lean | /-
Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kevin Buzzard
-/
import Mathlib.Order.Filter.AtTopBot.Basic
import Mathlib.RingTheory.Finiteness.Basic
/-!
# Noetherian rings and modules
The following... |
IsPrimary.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.LinearAlgebra.Quotient.Basic
import Mathlib.RingTheory.Ideal.Operations
/-!
# Primary submodules
A proper submodule `S : Submodule R M` is primary ... |
QuadraticModuleCat.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.QuadraticForm.IsometryEquiv
import Mathlib.Algebra.Category.ModuleCat.Basic
/-!
# The category of quadratic modules
-/
open CategoryTheory
u... |
Factorization.lean | /-
Copyright (c) 2022 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import Mathlib.Order.Filter.Cofinite
import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
import Mathlib.RingTheory.UniqueFactorizati... |
Ideal.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.LocalRing.ResidueField.Basic
import Mathlib.RingTheory.Localization.AtPrime.Basic
import Mathlib.RingTheory.Localization.FractionRing
/-!
# The r... |
Basis.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.Algebra.DirectSum.Module
import Mathlib.LinearAlgebra.Finsupp.VectorSpace
/-!
# Bases for direct sum of modules
This file defines a `Module.Free` i... |
FriendshipGraphs.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Jalex Stark, Kyle Miller
-/
import Mathlib.Combinatorics.SimpleGraph.AdjMatrix
import Mathlib.LinearAlgebra.Matrix.Charpoly.FiniteField
/-!
# The Friendship Theorem
#... |
PartitionFiltration.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.MeasurableSpace.CountablyGenerated
import Mathlib.Probability.Process.Filtration
/-!
# Filtration built from the finite partitions of a coun... |
Functor.lean | /-
Copyright (c) 2024 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
import Mathlib.CategoryTheory.Grothendieck
/-!
# Structured Arrow Categories as strict functor to Cat
... |
Limits.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.Algebra.Pi
import Mathlib.Algebra.Algebra.Shrink
import Mathlib.Algebra.Category.AlgCat.Basic
import Mathlib.Algebra.Category.ModuleCat.Basic
impor... |
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