filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
all_order.v | Require Export order.
|
Basic.lean | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.NumberTheory.Cyclotomic.Rat
import Mathlib.NumberTheory.NumberField.Units.Basic
/-!
# Basic results on integral ideals of a number field
We study resul... |
Constructions.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, Patrick Massot
-/
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Finset.Piecewise
import Mathlib.Or... |
fingroup.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 div path... |
lakefile.lean | import Lake
open Lake DSL
/-!
## Mathlib dependencies on upstream projects
-/
require "leanprover-community" / "batteries" @ git "main"
require "leanprover-community" / "Qq" @ git "master"
require "leanprover-community" / "aesop" @ git "master"
require "leanprover-community" / "proofwidgets" @ git "v0.0.71" -- Proof... |
Bezout.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.RingTheory.PrincipalIdealDomain
/-!
# Bézout rings
A Bézout ring (Bezout ring) is a ring whose finitely generated ideals are principal.
Notable examples i... |
Encodable.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.DFinsupp.Defs
import Mathlib.Logic.Encodable.Pi
/-!
# `Encodable` and `Countable` instances for `Π₀ i, α i`
In this file we provide instances f... |
Coord.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.Analysis.Calculus.AddTorsor.AffineMap
import Mathlib.Analysis.Normed.Affine.AddTorsorBases
/-!
# Barycentric coordinates are smooth
-/
variable {ι 𝕜 E P :... |
imset2_finset.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Check @imset2_pair.
|
Coinvariants.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.Algebra.Homology.ShortComplex.ModuleCat
import Mathlib.RepresentationTheory.Rep
/-!
# Coinvariants of a group representation
Given a commutativ... |
div.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.
(******************************************************************************)
(* Th... |
Rename.lean | /-
Copyright (c) 2021 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner
-/
import Lean.Elab.Tactic.ElabTerm
import Mathlib.Init
/-!
# The `rename'` tactic
The `rename'` tactic renames one or several hypotheses.
-/
namespace Mathlib.Tactic
o... |
ToApp.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.Util.AddRelatedDecl
/-!
# The `to_app` attribute
Adding `@[to_app]` to a lemma named `F` of shape `∀ .., η = θ`,... |
path.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(******************************************************************************)
(* ... |
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... |
IsSheafOneHypercover.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Sites.OneHypercover
/-!
# Characterization of sheaves using 1-hypercovers
In this file, given a Grothendieck topology `J` on a category `C`,
we ... |
DivMod.lean | /-
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Mario Carneiro
-/
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Tactic.NormNum.Ineq
/-!
# `norm_num` extension for integer div/mod and divides
This file adds support f... |
SeminormFromBounded.lean | /-
Copyright (c) 2024 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.Analysis.Normed.Unbundled.RingSeminorm
/-!
# seminormFromBounded
In this file, we prove [BGR, Proposition 1.2.1/2][bos... |
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... |
FinTopCat.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.CategoryTheory.FintypeCat
import Mathlib.Topology.Category.TopCat.Basic
/-!
# Category of finite topological spaces
Definition of the category of... |
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.Ring.Basic
/-!
# WithAbs
`WithAbs v` is a type synonym for a semiring `R` which depends on an absolute value. The point of
this... |
CompactOpen.lean | /-
Copyright (c) 2018 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import Mathlib.Topology.Hom.ContinuousEval
import Mathlib.Topology.ContinuousMap.Basic
import Mathlib.Topology.Separation.Regular
/-!
# The compact-open topology
In this ... |
FactorSet.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.Data.Finsupp.Multiset
import Mathlib.RingTheory.UniqueFactorizationDomain.Basic
import Mathlib.Tactic.Ring
/-!
# Set o... |
WittPolynomial.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Algebra.MvPolynomial.Variables
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Alg... |
DiscreteUniformity.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: Johannes Hölzl, Mario Carneiro, Antoine Chambert-Loir, María Inés de Frutos Fernández
-/
import Mathlib.Topology.UniformSpace.Basic
/-! # Discre... |
Basic.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Data.PFunctor.Univariate.M
/-!
# Quotients of Polynomial Functors
We assume the following:
* `P`: a polynomial functor
* `W`: its W-type
* `M`: its M... |
Hydra.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.Finsupp.Lex
import Mathlib.Data.Finsupp.Multiset
import Mathlib.Order.GameAdd
/-!
# Termination of a hydra game
This file deals with the following version... |
Basic.lean | /-
Copyright (c) 2023 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, Moritz Firsching, Michael Stoll
-/
import Mathlib.Algebra.Group.EvenFunction
import Mathlib.Data.ZMod.Units
import Mathlib.NumberTheory.MulChar.Basic
/-!
# Dirichl... |
Associator.lean | /-
Copyright (c) 2025 Bernhard Reinke. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bernhard Reinke
-/
import Mathlib.Algebra.Ring.Basic
import Mathlib.Tactic.Abel
/-!
# Associator in a ring
If `R` is a non-associative ring, then `(x * y) * z - x * (y * z)` is cal... |
Definability.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.ModelTheory.Definability
import Mathlib.RingTheory.MvPolynomial.FreeCommRing
import Mathlib.RingTheory.Nullstellensatz
import Mathlib.ModelTheory.Algebra.... |
TopologicalSimplex.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Adam Topaz
-/
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.AlgebraicTopology.SimplexCategory.Basic
import Mathlib.Topology.Category.TopCat.Basic
import Ma... |
Reassoc.lean | /-
Copyright (c) 2022 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.Functor.Basic
import Mathlib.Lean.Meta.Simp
import Mathlib.Tactic.Simps.Basic
import Mathlib.Util.AddRelatedDecl
/-!
# The `... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
fraction.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 div seq.
From mathcomp Require Import ssrAC choice tuple ... |
PEquiv.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.Data.Option.Basic
import Batteries.Tactic.Congr
import Mathlib.Data.Set.Basic
import Mathlib.Tactic.Contrapose
/-!
# Partial Equivalences
In this file, ... |
Imo2021Q1.lean | /-
Copyright (c) 2021 Mantas Bakšys. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mantas Bakšys
-/
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
/-!
# IMO 2021 Q1
Let `n ≥ 100` be an integer. Ivan writes... |
Locus.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.Etale.Kaehler
import Mathlib.RingTheory.Spectrum.Prime.FreeLocus
import Mathlib.RingTheory.Support
/-!
# Smooth locus of an algebra
Most results... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
ContinuousOn.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Constructions
/-!
# Neighborhoods and continuity relative to a subset
This file develops API on the relative versions
* `nhdsWithin` ... |
Three.lean | /-
Copyright (c) 2024 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Sanyam Gupta, Omar Haddad, David Lowry-Duda,
Lorenzo Luccioli, Pietro Monticone, Alexis Saurin, Florent Schaffhauser
-/
import Mathlib.NumberTheory.FLT.Basic
import... |
Lint.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Batteries.Tactic.Lint
import Mathlib.Tactic.DeclarationNames
/-!
# Linters for Mathlib
In this file we define additional linters for mathlib,
which conce... |
Nat.lean | /-
Copyright (c) 2024 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
import Mathlib.Algebra.Order.Antidiag.Pi
import Mathlib.NumberTheory.ArithmeticFunction
import Mathlib.Tactic.IntervalCases
/-!
# Sets of tuples with a fixed pro... |
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... |
ExistsAndEq.lean | import Mathlib.Tactic.Simproc.ExistsAndEq
universe u
variable (α : Type u) (p q : α → Prop)
example (a : α) (hp : p a) (hq : q a) : ∃ b : α, (p b ∧ b = a) ∧ q b := by
simp only [existsAndEq]
guard_target = (p a ∧ True) ∧ q a
exact ⟨⟨hp, trivial⟩, hq⟩
example (a : α) : ∃ b : α, b = a := by
simp only [existsAn... |
Basic.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.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.GroupTheory.Congruence.Hom
import Mathli... |
Final.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Jakob von Raumer
-/
import Mathlib.CategoryTheory.Category.Cat.AsSmall
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
import Mathlib.CategoryTheory.IsConnected
i... |
HomCongr.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.CategoryTheory.Iso
/-!
# Conjugate morphisms by isomorphisms
We define
`CategoryTheory.Iso.homCongr : (X ≅ X₁) → (Y ≅ Y₁) → (X ⟶ Y) ≃ (X₁ ⟶ Y₁)`,
c... |
Killing.lean | /-
Copyright (c) 2024 Frédéric Marbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Marbach
-/
import Mathlib.Algebra.Lie.Derivation.AdjointAction
import Mathlib.Algebra.Lie.Killing
import Mathlib.LinearAlgebra.BilinearForm.Orthogonal
/-!
# Derivations of ... |
numfield.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 ssrAC div fintyp... |
Two.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.CharP.Lemmas
import Mathlib.GroupTheory.OrderOfElement
/-!
# Lemmas about rings of characteristic two
This file contains results about `CharP R 2`,... |
Shatter.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.Combinatorics.SetFamily.Compression.Down
import Mathlib.Data.Fintype.Powerset
import Mathlib.Order.Interval.Finset.Nat
import Mathlib.Algebra.BigOperators.... |
ENat.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Order.Hom.Ring
import Mathlib.Data.ENat.Basic
import Mathlib.SetTheory.Cardinal.Basic
/-!
# Conversion between `Cardinal` and `ℕ∞`
In this ... |
Probability.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.MeasureTheory.Measure.Typeclasses.Finite
/-!
# Classes for probability measures
We introduce the following typeclasses for measures:
... |
CyclotomicCharacter.lean | /-
Copyright (c) 2023 Hanneke Wiersema. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Hanneke Wiersema, Andrew Yang
-/
import Mathlib.Algebra.Ring.Aut
import Mathlib.NumberTheory.Padics.RingHoms
import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity
... |
BigOperators.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import Mathlib.Algebra.Module.Submodule.Basic
import Mathlib.RingTheory.Ideal.Defs
/-!
# Big operators for ideals
This contains some results on... |
choice.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.
(**************************************************... |
all_order.v | Require Export order.
|
recover.lean | import Mathlib.Tactic.Recover
set_option linter.unusedTactic false
/-- problematic tactic for testing recovery -/
elab "this" "is" "a" "problem" : tactic =>
Lean.Elab.Tactic.setGoals []
/- The main test -/
example : 1 = 1 := by
recover this is a problem
rfl
/- Tests that recover does no harm -/
example : 3 < ... |
EckmannHilton.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kenny Lau, Robert Y. Lewis
-/
import Mathlib.Algebra.Group.Defs
/-!
# Eckmann-Hilton argument
The Eckmann-Hilton argument says that if a type carries two monoid structures... |
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.Data.Set.Pairwise.Basic
import Mathlib.Data.SetLike.Basic
import Mathlib.Order.Directed
import Mathlib.Order.Hom.Set
/-!
# Chains and flags
This file... |
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.Polynomial.Degree.Definitions
import Mathlib.Algebra.Polynomial.Monomial
import Mathlib.Data.Nat.Succ... |
IsOpenComapC.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.RingTheory.Polynomial.Basic
import Mathlib.RingTheory.Spectrum.Prime.Topology
/-!
The morphism `Spec R[x] --> Spec R` induced by the natural inclusion `... |
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.
(**********************... |
Algebra.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.Defs
import Mathlib.Algebra.Order.Module.OrderedSMul
/-!
# Ordered algebras
An ordered algebra is an ordered semiring, which is an algebr... |
Defs.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.RingTheory.IntegralClosure.IsIntegral.Defs
/-!
# Integral closure as a characteristic predicate
## Main definitions
Let `R` be a `CommRing` and let `A` be an ... |
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... |
Operations.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.EReal.Basic
/-!
# Addition, negation, subtraction and multiplication on extended real numbers
Addition and multiplication in `EReal` are problemat... |
Elements.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Comma.StructuredArrow.Basic
import Mathlib.CategoryTheory.Category.Cat
/-!
# The category of elements
This file defines the category of el... |
Basic.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
-/
import Mathlib.Tactic.Attr.Register
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.Basic
import Batteries.Logic
import Batteries.Tactic.T... |
Different.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.NumberTheory.KummerDedekind
import Mathlib.NumberTheory.RamificationInertia.Unramified
import Mathlib.RingTheory.Finiteness.Quotient
import Mathlib.RingTheor... |
gproduct.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 bigo... |
Quotient.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.Tactic.Common
/-!
# Algebraic quotients
This file defines notation for algebraic quotients, e.g. quotient groups `G ⧸ H`,
quotient modules `M ⧸ N` and idea... |
Square.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.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square
/-!
# Relation between pullback/pushout squares and kernel/cokernel sequence... |
Ultra.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.Analysis.Normed.Field.Basic
import Mathlib.Analysis.Normed.Ring.Ultra
import Mathlib.Data.Nat.Choose.Sum
/-!
## Conditions to have an ultrametric no... |
OrderOfElement.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Julian Kuelshammer
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.Algebra.Group.Pointwise.Set.Finite
import Mathlib.Alge... |
Injective.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Kim Morrison
-/
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Preadditive.Injective.Basic
import Mathlib.Algebra.Category.Grp.EpiMo... |
all_fingroup.v | From mathcomp Require Export action.
From mathcomp Require Export automorphism.
From mathcomp Require Export fingroup.
From mathcomp Require Export gproduct.
From mathcomp Require Export morphism.
From mathcomp Require Export perm.
From mathcomp Require Export presentation.
From mathcomp Require Export quotient.
|
Pi.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.Fintype.Pi
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-!
# Products over `univ.pi`
-/
assert_not_exists MonoidWithZero MulAction O... |
norm_cast.lean | /-
Tests for norm_cast
-/
import Mathlib.Tactic.Ring
import Mathlib.Data.Complex.Basic
import Mathlib.Data.ENNReal.Inv
-- set_option trace.Tactic.norm_cast true
-- set_option trace.Meta.Tactic.simp true
set_option autoImplicit true
set_option linter.unusedVariables false
variable (an bn cn dn : ℕ) (az bz cz dz : ℤ)
... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
StructureSheaf.lean | /-
Copyright (c) 2020 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.Category.Ring.Colimits
import Mathlib.Algebra.Category.Ring.Instances
import Mathlib.Algebra.Category.Ring.Limits
import Mathlib.Al... |
Mon_.lean | /-
Copyright (c) 2025 Markus Himmel, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Andrew Yang
-/
import Mathlib.Algebra.Category.MonCat.Limits
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
import Mathlib.CategoryTheory.Monoidal.Mo... |
Base.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.Chain
import Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas
import Mathlib.LinearAlgebra.RootSystem.IsValuedIn
/-!
# Bases for root... |
test_rat.v | From mathcomp Require Import all_boot all_order all_algebra.
Local Open Scope ring_scope.
Goal 2%:Q + 2%:Q = 4%:Q.
Proof. reflexivity. Qed.
Goal - 2%:Q = -1 * 2%:Q.
Proof. reflexivity. Qed.
Goal 2%:Q ^+ 2 = 4%:Q.
Proof. reflexivity. Qed.
Goal (-1)^-1 = -1 :> rat.
Proof. reflexivity. Qed.
Local Open Scope rat_scop... |
Unitary.lean | /-
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shing Tak Lam, Frédéric Dupuis
-/
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.Algebra.Star.SelfAdjoint
import Mathlib.Algebra.Algebra.Spectrum.Basic
import Mathli... |
ResidueField.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.Geometry.RingedSpace.LocallyRingedSpace
import Mathlib.RingTheory.LocalRing.ResidueField.Basic
/-!
# Residue fields of points
Any point `x` of a... |
Maps.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.MeasurableSpace.Embedding
import Mathlib.Order.Restriction
/-! # Auxiliary maps for Ionescu-Tulcea theorem
This file contains auxiliary... |
SInteger.lean | /-
Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.RingTheory.DedekindDomain.AdicValuation
/-!
# `S`-integers and `S`-units of fraction fields of Dedekind domains
Let `K` be the fi... |
Dioph.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.Fin.Fin2
import Mathlib.Data.PFun
import Mathlib.Data.Vector3
import Mathlib.NumberTheory.PellMatiyasevic
/-!
# Diophantine functions and Matiyas... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
Defs.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Gabriel Ebner
-/
import Mathlib.Data.Nat.Cast.Defs
/-!
# Cast of integers
This file defines the *canonical* homomorphism from the integers into an
additive group with... |
SelmerGroup.lean | /-
Copyright (c) 2022 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.Group.Equiv.TypeTags
import Mathlib.Data.ZMod.QuotientGroup
import Mathlib.RingTheory.DedekindDomain.AdicValuation
import M... |
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... |
NormalizedFactors.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.Algebra.GCDMonoid.Basic
import Mathlib.Data.Multiset.OrderedMonoid
import Mathlib.RingTheory.UniqueFactorizationDomain.... |
presentation.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.
From mathcomp Require Import fintype finset fingroup morphism.
(**********************... |
Completion.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.Topology.Algebra.Nonarchimedean.Basic
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.Algebra.UniformRing
/-!
# The completion of ... |
Summable.lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.Ring.Action.Rat
import Mathlib.RingTheory.HahnSeries.Multiplication
import Mathlib.Data.Rat.Cast.Lemmas
/-!
# Summable families of Hahn Series... |
Monad.lean | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Monad Operations for Probability Mass Functions
This file constructs two operations on `PMF` ... |
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) 2025 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.VariableChange
/-!
# Weierstrass equations and the non... |
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