filename stringlengths 5 42 | content stringlengths 15 319k |
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perm.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 tup... |
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... |
Nonarchimedean.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Algebra.Group.Subgroup.Finite
import Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.T... |
FreydMitchell.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.GrothendieckCategory.ModuleEmbedding.Opposite
import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Indization
/-!
# The Freyd... |
Sets.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.Finset.BooleanAlgebra
import Mathlib.Data.Finset.SymmDiff
import Mathlib.Data.Fintype.OfMap
/-!
# Subsets of finite types
In a `Fintype`, all `S... |
ClearExcept.lean | /-
Copyright (c) 2022 Joshua Clune. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joshua Clune
-/
import Mathlib.Init
import Lean.Elab.Tactic.ElabTerm
/-!
# The `clear*` tactic
This file provides a variant of the `clear` tactic, which clears all hypotheses it can
be... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.BigOperators... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Implicit.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv
import Mathlib.Analysis.Calculus.FDeriv.Add
import Mathlib.Analysis.Calculus.FDeriv.Prod
import Mathl... |
preorder.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... |
ETransform.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import Mathlib.Algebra.Ring.Nat
/-!
# e-transforms
e-transforms are a family of transformations of pairs of finite ... |
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.Algebra.Group.Equiv.TypeTags
import Mathlib.Algebra.Order.Hom.Monoid
import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags
/-!
# Order Monoid Isom... |
Imo1977Q6.lean | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib.Data.PNat.Basic
/-!
# IMO 1977 Q6
Suppose `f : ℕ+ → ℕ+` satisfies `f(f(n)) < f(n + 1)` for all `n`.
Prove that `f(n) = n` for all `n`.
We first prove the prob... |
InitialSeg.lean | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Order.InitialSeg
import Mathlib.Order.SuccPred.Limit
/-!
# Initial segments and successors
We establish some connections betw... |
Height.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wanyi He, Jiedong Jiang, Jingting Wang, Andrew Yang, Shouxin Zhang
-/
import Mathlib.Algebra.Module.SpanRank
import Mathlib.RingTheory.Spectrum.Prime.Noetherian
import Mathlib.RingTheory.... |
Exception.lean | /-
Copyright (c) 2022 Edward Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward Ayers
-/
import Mathlib.Init
import Lean.Exception
/-!
# Additional methods for working with `Exception`s
This file contains two additional methods for working with `Exception`s... |
Eval.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Johan Commelin, Mario Carneiro
-/
import Mathlib.Algebra.MvPolynomial.Basic
/-!
# Multivariate polynomials
This file defines functions for evaluating multivariate pol... |
Topology.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.MeasureTheory.Measure.Typeclasses.NoAtoms
import Mathlib.Topology.DiscreteSubset
/-!
# Theorems combining measure theory and topology
This file gathe... |
HomologicalComplex.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.Homology.ComplexShape
import Mathlib.CategoryTheory.Subobject.Limits
import Mathlib.CategoryTheory.GradedObject
import Mathlib.Alge... |
MatrixAlgebra.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Eric Wieser
-/
import Mathlib.Data.Matrix.Basis
import Mathlib.Data.Matrix.Composition
import Mathlib.Data.Matrix.Kronecker
import Mathlib.RingTheory.TensorProduct.Basic
... |
Reduce.lean | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Mario Carneiro
-/
import Mathlib.Computability.Halting
/-!
# Strong reducibility and degrees.
This file defines the notions of computable many-one reduction and one-one
reduc... |
finset.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 div seq.
From mathcomp Require Import choice fintype finf... |
Basic.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.Fin.VecNotation
import Mathlib.Data.SetLike.Basic
import Mathlib.Logic.Small.Basic
import Mathlib.SetTheory.ZFC.PSet
/-!
# A model of ZFC
In thi... |
SorgenfreyLine.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.Monotone
import Mathlib.Topology.Instances.Irrational
import Mathlib.Topology.Algebra.Order.Archimedean
import Mathlib.Topology.Co... |
OptionalStopping.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.Probability.Process.HittingTime
import Mathlib.Probability.Martingale.Basic
/-! # Optional stopping theorem (fair game theorem)
The optional stopping theor... |
Basic.lean | /-
Copyright (c) 2019 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Group.Units.Defs
import Mathlib.Algebra.BigOperators.Group.List.Basic
import Mathlib.Algebr... |
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... |
NodupEquivFin.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.Data.List.Duplicate
import Mathlib.Data.List.Sort
/-!
# Equivalence between `Fin (length l)` and elements of a list
Given a list `l`,
* if `l` has... |
LinearTopology.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández, Anatole Dedecker
-/
import Mathlib.RingTheory.TwoSidedIdeal.Operations
import Mathlib.Top... |
Basic.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Robin Carlier
-/
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.Quotient
import Mathlib.Combinatorics.Quiver.Path
/-!
# The category paths on a quiver... |
Sigma.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Set.Image
import Mathlib.Data.Set.BooleanAlgebra
/-!
# Sets in sigma types
This file defines `Set.sigma`, the indexed sum of sets.
-/
namespace Set... |
Variance.lean | import Mathlib.Probability.Moments.Variance
deprecated_module (since := "2025-05-16")
|
Monomial.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Group.Nat.Hom
import Mathlib.Algebra.Polynomial.Basic
/-!
# Univariate monomials
-/
noncomputable ... |
Subobject.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.Subpresheaf.Image
import Mathlib.CategoryTheory.Subobject.Basic
/-!
# Comparison between `Subpresheaf`, `MonoOver` and `Subobject`
Given a presh... |
SetAlgebra.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.Data.Finite.Prod
import Mathlib.MeasureTheory.SetSemiring
/-!
# Algebra of sets
In this file we define the notion of algebra of sets and give its bas... |
Change.lean | import Mathlib.Tactic.Change
set_option linter.style.setOption false
set_option pp.unicode.fun true
set_option autoImplicit true
/--
info: Try this: change 0 = 1
---
info: Try this: change (fun x ↦ x) 0 = 1
---
info: Try this: change (fun x ↦ x) 0 = 1
---
error: The term
1 = 0
is not defeq to the goal:
(fun x ↦ x... |
galois.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
Defs.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.GroupWithZero.Hom
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.Algebra.Ring.Defs
import Mathlib.Data.Nat.Lattice
/-!
# Definition... |
Dedup.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.Dedup
import Mathlib.Data.Multiset.UnionInter
/-!
# Erasing duplicates in a multiset.
-/
assert_not_exists Monoid
namespace Multiset
open... |
Pi.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.Vector.Basic
import Mathlib.Logic.Equiv.Finset
/-!
# Encodability of Pi types
This file provides instances of `Encodable` for types of vectors a... |
KernelCokernelComp.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.Algebra.Homology.ShortComplex.SnakeLemma
/-!
# Long exact sequence for the kernel and cokernel of a composition
If `f : X ⟶ Y` and `g : Y ⟶ Z` are composable m... |
Pseudofunctor.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.Join.Basic
import Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor
/-!
# Pseudofunctoriality of categorical joins
In this file, w... |
Action.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Tactic.Ca... |
BuffonsNeedle.lean | /-
Copyright (c) 2024 Enrico Z. Borba. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Enrico Z. Borba
-/
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Mathlib.MeasureTheory.Integral.Prod
import Mathlib.Probability.Density
import Mathlib.Probability.D... |
ValuativeRel.lean | /-
Copyright (c) 2025 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Liu, Adam Topaz
-/
import Mathlib.RingTheory.Valuation.Basic
import Mathlib.Data.NNReal.Defs
import Mathlib.Topology.Defs.Filter
/-!
# Valuative Relations
In this file we introduc... |
Units.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-- Some proofs and docs came from mathlib3 `src/algebra/commute.lean` (c) Neil Strickland
import Mathlib.Algebra.Group.Semiconj.Defs
import Mathlib.Algebra.Group.U... |
Basic.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.Data.Nat.Init
import Mathlib.Logic.Nontrivial.Defs
import Mathlib.... |
Submonoid.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Algebra.Group.Submonoid.BigOperators
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Data.DFinsupp.BigOperators
import Mathlib.O... |
Synonym.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Order.Synonym
/-!
# Group structure on the order type synonyms
Transfer algebraic instances from `α... |
TypeTags.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.O... |
Rank.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.Free
import Mathlib.LinearAlgebra.Dimension.Subsingleton
import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
/-!
# Some results on th... |
Centralizer.lean | /-
Copyright (c) 2021 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Algebra.Ring.Defs
/-!
# Centralizers of rings
-/
assert_not_exists RelIso
variable {M : Type*} ... |
AsSubring.lean | /-
Copyright (c) 2022 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Junyan Xu
-/
import Mathlib.RingTheory.Localization.LocalizationLocalization
import Mathlib.LinearAlgebra.FreeModule.Basic
import Mathlib.Algebra.Algebra.Subalgebra.Tower
/-!
... |
Rotate.lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.CategoryTheory.Triangulated.Basic
/-!
# Rotate
This file adds the ability to rotate triangles a... |
Imo2005Q4.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.FieldTheory.Finite.Basic
/-!
# IMO 2005 Q4
Problem: Determine all positive integers relatively prime to all the terms of the infinite sequence
`a n... |
SumPrimeReciprocals.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.Algebra.Order.Group.Indicator
import Mathlib.Analysis.PSeries
import Mathlib.NumberTheory.SmoothNumbers
/-!
# The sum of the reciprocals of the primes d... |
Rat.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Action.Defs
/-!
# Actions by nonnegative rational numbers
-/
assert_not_exists ... |
CoherenceLemmas.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta, Jakob von Raumer
-/
import Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence
/-!
# Lemmas which are consequences of monoidal coher... |
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... |
SnakeLemma.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Algebra.Exact
/-!
# The snake lemma in terms of modules
The snake lemma is proven in `Mathlib/Algebra/Homology/ShortComplex/SnakeLemma.lean` for all abeli... |
Semiquot.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.Set.Lattice
/-! # Semiquotients
A data type for semiquotients, which are classically equivalent to
nonempty sets, but are useful for programming... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
Topology.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Strict
import Mathlib.Topology.Algebra.Affine
import Mathlib.Topology.... |
Grothendieck.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.Limits.FunctorCategory.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Grothendieck
/-!
# Colimits on Grothendieck constructions ... |
Identities.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.Frobenius
import Mathlib.RingTheory.WittVector.Verschiebung
import Mathlib.RingTheory.WittVector.MulP
/-!
## Identities between ... |
TermCongr.lean | import Mathlib.Tactic.TermCongr
/-!
`congr(...)` tests needing no additional imports
-/
namespace Tests
set_option autoImplicit true
--set_option trace.Elab.congr true
section congr_thms
/-! Tests that `congr(...)` subsumes `congr_arg`/`congr_fun`/`congr`.
Uses `(... :)` to make sure `congr(...)` is not seeing exp... |
Basic.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.Abelian.Basic
import Mathlib.CategoryTheory.ObjectProperty.ContainsZero
import Mathlib.CategoryTheory.ObjectProperty.EpiMono
import Mathlib.Catego... |
Aut.lean | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Ring.AddAut
import Mathlib.Data.ZMod.Basic
/-!
# Automorphism Group of `ZMod`.
-/
assert_not_exists Field TwoSidedIdeal
namespace ZMod
va... |
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.
(**********************... |
CompileInductive.lean | import Mathlib.Util.CompileInductive
import Mathlib.Data.Fin.Fin2
compile_inductive% Fin2
example := @Nat.rec
example := @List.rec
example := @Fin2.rec
example := @PUnit.rec
example := @PEmpty.rec
example := @Nat.recOn
example := @List.recOn
example := @Fin2.recOn
example := @PUnit.recOn
example := @PEmpty.recOn
exa... |
Order.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Ruben Van de Velde
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Group.Subsemigroup.Operations
import Mathlib.Algebra.Order.Group.Unbundled.Abs
im... |
Defs.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Opposites
import Mathlib.Tactic.Spread
/-!
# Definitions of group actions
This file de... |
Push.lean | /-
Copyright (c) 2022 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Prefunctor
/-!
# Pushing a quiver structure along a map
Given a map `σ : V → W` and a `Quiver` instance on `V`, this files de... |
CongrM.lean | /-
Copyright (c) 2023 Moritz Doll, Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Gabriel Ebner, Damiano Testa, Kyle Miller
-/
import Mathlib.Tactic.TermCongr
import Mathlib.Tactic.WithoutCDot
/-!
# The `congrm` tactic
The `congrm` tactic ... |
Compact.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.LinearAlgebra.Finsupp.LinearCombination
import Mathlib.RingTheory.Finiteness.Defs
import Mathlib.Topology.Algebra.Ring.Basic
import Mathlib.RingTheory.Noethe... |
ExtraDegeneracy.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.AlternatingFaceMapComplex
import Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
import Mathlib.AlgebraicTopology.CechNerve
import Mathlib.A... |
Double.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.HasNoLoop
import Mathlib.Algebra.Homology.Single
import Mathlib.CategoryTheory.Yoneda
/-!
# A homological complex lying in two degrees
Given `... |
WithLp.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.Data.ENNReal.Basic
import Mathlib.RingTheory.Finiteness.Defs
/-! # The `WithLp` type synonym
`WithLp p V` is a copy of `V` with exactly the same vector spa... |
OfScientific.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Thomas Murrills
-/
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Data.Rat.Cast.Lemmas
/-!
## `norm_num` plugin for scientific notation.
-/
namespace Mathlib
open... |
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.Defs
import Mathlib.Algebra.GroupWithZero.Action.Basic
import Mathlib.Algebra.Module.End
import Mathlib.Data.Rat.Cast.CharZero
... |
Subcanonical.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.Limits.Preserves.Ulift
import Mathlib.CategoryTheory.Sites.Canonical
import Mathlib.CategoryTheory.Sites.Whiskering
/-!
# Subcanoni... |
ENNRealLogExp.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Analysis.SpecialFunctions.Log.ERealExp
import Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog
import M... |
Types.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.Closed.Cartesian
import Mathlib.CategoryTheory.Limits.Presheaf
import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory
import Mathl... |
CoeffMem.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.Algebra.Algebra.Operations
import Mathlib.Algebra.Polynomial.Div
import Mathlib.RingTheory.Ideal.Span
/-!
# Bounding the coeffic... |
CovarianceBilin.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Analysis.LocallyConvex.ContinuousOfBounded
import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
import Mathlib.Probability.Moments.Var... |
Matrix.lean | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee
-/
import Mathlib.Data.Matrix.Notation
import Mathlib.LinearAlgebra.Matrix.Symmetric
/-!
# Coxeter matrices
Let us say that a matrix (possibly an infinite ... |
JacobianOneDim.lean | /-
Copyright (c) 2025 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.Deriv.Slope
import Mathlib.MeasureTheory.Function.Jacobian
/-!
# Change of variable formulas for integrals in dimension 1
We ... |
Delaborator.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Init
import Lean.PrettyPrinter.Delaborator.Basic
/-!
# Additions to the delaborator
-/
namespace Lean.PrettyPrinter.Delaborator
open SubExpr
/-- Assuming... |
SymplecticGroup.lean | /-
Copyright (c) 2022 Matej Penciak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matej Penciak, Moritz Doll, Fabien Clery
-/
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
# The Symplectic Group
This file defines the symplectic group and proves element... |
AddChar.lean | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.NumberTheory.Padics.MahlerBasis
import Mathlib.Topology.Algebra.Monoid.AddChar
import Mathlib.Analysis.SpecificLimits.Normed
/-!
# Additive characters... |
BigOperators.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Yaël Dillies
-/
import Mathlib.Algebra.Field.GeomSum
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Alg... |
Defs.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.OfNat
/-!
# Cast of natural numbers
This file defines the *can... |
Affine.lean | /-
Copyright (c) 2023 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.Algebra.Polynomial.Bivariate
import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass
import Mathlib.AlgebraicGeometry.EllipticCu... |
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.
(*****... |
Preimage.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.Finset.Pi
import Mathlib.Data.Finset.Sigma
import Mathlib.Data.Finset.Sum
import Mathlib.Data.Set.Finite.Basic
/-!
# Preimage of ... |
NatInt.lean | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.EuclideanDomain.Int
import Mathlib.Algebra.Order.Ring.Int
import Mathlib.Data.Nat.Prime.Int
import Mathlib.RingTheory.Int.Basic
import Mathlib.RingTheory... |
Basic.lean | /-
Copyright (c) 2019 Kim Morrison, Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Simon Hudon, Adam Topaz, Robin Carlier
-/
import Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts
import Mathlib.CategoryTheory.Limits... |
FieldDivision.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Order.Group.Finset
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Algebra.Polynomial.Eva... |
Transitive.lean | /-
Copyright (c) 2022 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.GroupTheory.GroupAction.Defs
import Mathlib.GroupTheory.GroupAction.Hom
/-! # Complements to pretransitive actions
When `f : X →ₑ[φ] Y`... |
Types.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.CategoryTheory.Subobject.WellPowered
import Mathlib.CategoryTheory.Types
import Mathlib.Data.Set.Subsingleton
/-!
# `Type u` is well-powered
By building ... |
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