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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 ...
NatLog.lean
/- Copyright (c) 2024 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Andreas Gittis -/ import Mathlib.Data.Nat.Log import Mathlib.Tactic.NormNum /-! # `norm_num` extensions for `Nat.log` and `Nat.clog` This module defines `norm_num` extensio...
Discrete.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Topology.Order.Basic import Mathlib.Order.SuccPred.LinearLocallyFinite /-! # Instances related to the discrete topology We prove that the discrete topolo...
Density.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Group.Pointwise.Finset.Scalar import Mathlib.Algebra.Group.Action.Pointwise.Finset import Mathlib.Algebra.Group.Action.Defs i...
Defs.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Algebra.AddTorsor.Defs /-! # Affine space In this file we introduce the following notation: * `AffineSpace V P` is an alternative notation for `AddTorso...
Enough.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.EffectiveEpi.Basic /-! # Effectively enough objects in the image of a functor We define the class `F.EffectivelyEnough` on a funct...
extremal.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...
Homotopies.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.Algebra.Homology.Homotopy import Mathlib.AlgebraicTopology.DoldKan.Notations /-! # Construction of homotopies for the Dold-Kan correspondence (The general str...
Quantale.lean
/- Copyright (c) 2024 Pieter Cuijpers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Pieter Cuijpers -/ import Mathlib.Algebra.Group.Defs import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Order.CompleteLattice.Basic import Mathlib.Tactic.Variable /-!...
cases.lean
import Batteries.Logic import Mathlib.Tactic.Cases import Mathlib.Data.Nat.Notation set_option autoImplicit true example (x : α × β × γ) : True := by cases' x with a b; cases' b with b c guard_hyp a : α guard_hyp b : β guard_hyp c : γ trivial example {α β γ : Type u} (x : α × β × γ) : True := by cases' h:...
Diagonal.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.LinearAlgebra.Dimension.LinearMap import Mathlib.LinearAlgebra.Matrix.ToLin /-! # Diagonal matrices This fi...
GetD.lean
/- Copyright (c) 2024 Bolton Bailey. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bolton Bailey, Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro -/ import Mathlib.Data.List.Defs import Mathlib.Data.Option.Basic import Mathlib.Util...
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...
Seminorm.lean
/- Copyright (c) 2022 María Inés de Frutos-Fernández, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Yaël Dillies -/ import Mathlib.Data.NNReal.Defs import Mathlib.Order.ConditionallyCompleteLattice.Group /-! # Group semin...
orderedzmod.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...
Inverse.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau, María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.RingTheory.DiscreteValuationRing.Basi...
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...
DivPairs.lean
/- Copyright (c) 2025 Yaël Dillies, Michał Mrugała. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Michał Mrugała -/ import Mathlib.GroupTheory.MonoidLocalization.Basic /-! # Submonoid of pairs with quotient in a submonoid This file defines the submonoi...
Real.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Topology.ContinuousMap.Basic import Mathlib.Topology.MetricSpace.Cauchy /-! # The reals are complete This file provides the instances...
finalg.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 finset f...
Defs.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.Group.Defs import Mathlib.Logic.Nontrivial.Defs import Mathlib.Tactic.SplitIfs import Mathlib.Logic.Basic /-! # Typeclasses for groups with an...
Isometry.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.Basic /-! # Isometric linear maps ## Main definitions * `QuadraticMap.Isometry`: `LinearMap`s which map between two different ...
Lawful.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sebastian Ullrich -/ import Mathlib.Tactic.Basic /-! # Functor Laws, applicative laws, and monad Laws -/ universe u v namespace StateT section variable {σ : Type u} variab...
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.
Hom.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Hom.CompleteLattice import Mathlib.Order.UpperLower.Principal /-! # `UpperSet.Ici` etc as `Sup`/`sSup`/`Inf`/`sInf`-homomorphisms In t...
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.
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...
Quotients.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Data.Fintype.Quotient import Mathlib.ModelTheory.Semantics /-! # Quotients of First-Order Structures This file defines prestructures and quotients of...
CompactOpen.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Nailin Guan -/ import Mathlib.Topology.Algebra.ContinuousMonoidHom import Mathlib.Topology.Algebra.Equicontinuity import Mathlib.Topology.Algebra.Group.Compact import...
gseries.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import fintype bigop finset fingroup morphism. From mathcomp...
Instances.lean
/- Copyright (c) 2022 Stuart Presnell. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stuart Presnell, Eric Wieser, Yaël Dillies, Patrick Massot, Kim Morrison -/ import Mathlib.Algebra.GroupWithZero.InjSurj import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra....
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, Aurélien Saue, Anne Baanen -/ import Mathlib.Tactic.NormNum.Inv import Mathlib.Tactic.NormNum.Pow import Mathlib.Util.AtomM /-! # `ring` tactic A tactic for solving e...
Basic.lean
/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson -/ import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog import Mathlib.Analysis.SpecialFunctions.NonIntegrable import Mathlib.Analysis.SpecialFunctions.Pow.Deriv...
FunctorHom.lean
/- Copyright (c) 2024 Jack McKoen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jack McKoen, Joël Riou -/ import Mathlib.CategoryTheory.Monoidal.FunctorCategory import Mathlib.CategoryTheory.Monoidal.Types.Basic import Mathlib.CategoryTheory.Enriched.Basic /-! # Int...
Basic.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 import Mathlib.Algebra.Polynomial.Expand import Mathlib.RingTheory.Adjoin.Polynomial import Mathlib.RingTheory.Finiten...
Shortlex.lean
/- Copyright (c) 2024 Hannah Fechtner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hannah Fechtner -/ import Mathlib.Data.List.Lex import Mathlib.Tactic.Linarith import Mathlib.Order.RelClasses /-! # Shortlex ordering of lists. Given a relation `r` on `α`, the sh...
EquivReindex.lean
/- Copyright (c) 2024 Michail Karatarakis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michail Karatarakis -/ import Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic /-! # Reindexed basis This file introduces an equivalence between the set of embeddings o...
Nat.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.Nat.Defs import Mathlib.Algebra.Order.Monoid.Canonic...
EnoughInjectives.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.CommSq import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda import Mathlib.CategoryTheory.Abelian.GrothendieckCategory...
Basic.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.Enriched.Basic import Mathlib.CategoryTheory.Monoidal.Types.Coyoneda /-! # Enriched ordinary categories If `V` is a monoidal category, a `V`-enr...
maximal.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 choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
DeprecateTo.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Lean.Meta.Tactic.TryThis import Mathlib.Lean.Expr.Basic import Mathlib.Tactic.Lemma import Std.Time.Format /-! # `deprecate to` -- a deprecation tool Writing ...
GCD.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kyle Miller, Eric Wieser -/ import Mathlib.Algebra.Ring.Divisibility.Basic import Mathlib.Data.Int.GCD import Mathlib.Tactic.NormNum /-! # `norm_num` extensions for GC...
MonotoneConvergence.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, Yury Kudryashov -/ import Mathlib.Topology.Order.Basic /-! # Bounded monotone sequences converge In this file we prove a few theorems of the form “if the range of a...
Defs.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.Defs /-! # The natural numbers form a monoid This ...
Lemmas.lean
/- Copyright (c) 2023 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck, Ruben Van de Velde -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Analysis.Calculus.Deriv.Mul import Mathlib.Analysis.Calculus.Deriv.Shift impor...
ac.lean
section CCAC1 example (a b c : Nat) (f : Nat → Nat) : f (a + b + c) = f (c + b + a) := by grind example (a b c : Nat) (f : Nat → Nat) : a + b = c → f (c + c) = f (a + b + c) := by grind end CCAC1 section CCAC2 example (a b c d : Nat) (f : Nat → Nat → Nat) : b + a = d → f (a + b + c) a = f (c + d) a := by gri...
Polyrith.lean
/- Copyright (c) 2022 Dhruv Bhatia. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dhruv Bhatia, Eric Wieser, Mario Carneiro, Thomas Zhu -/ import Mathlib.Tactic.LinearCombination /-! # polyrith Tactic In this file, the `polyrith` tactic is created. This tactic, wh...
Integral.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.Probability.Kernel.Composition.IntegralCompProd import Mathlib.Probability.Kernel.Disintegration.StandardBorel /-! # Lebesgue and Bochner integrals of con...
Closure.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Yaël Dillies -/ import Mathlib.Data.Set.BooleanAlgebra import Mathlib.Data.SetLike.Basic import Mathlib.Order.Hom.Basic /-! # Closure operators between preorders We defin...
OfSection.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.Yoneda /-! # The subpresheaf generated by a section Given a presheaf of types `F : Cᵒᵖ ⥤ Type w`...
Basic.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Ring.Associated import Mathlib.Algebra.Star.Unitary import Mathlib.RingTheory.PrincipalIdealDomain import Mathlib.Tactic.Ring import Mathlib.Al...
ColimitType.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.Functor.Basic import Mathlib.CategoryTheory.Types /-! # The colimit type of a functor to types Given a category `J` (with `J : Type u` and `[Cat...
Expect.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.BigOperators.Expect import Mathlib.Algebra.Module.Rat import Mathlib.Algebra.Order.BigOperators.Ring.Finset import Mathlib.Algebra.Order.Module.Fie...
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.
Markov.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import Mathlib.MeasureTheory.Integral.Lebesgue.Add /-! # Markov's inequality The classical form of Markov's inequality states that for a nonnegative...
Bitwise.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Num.Basic import Mathlib.Data.Vector.Basic /-! # Bitwise operations using binary representation of integers ## Definitions * bitwise ope...
Finset.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.Finset.Option import Mathlib.Data.Set.Lattice.Image /-! # Lattice operations on finsets This file is concerned with how big lattice or set opera...
finset_repr.lean
import Mathlib.Data.Finset.Sort run_cmd Lean.Elab.Command.liftTermElabM do unsafe guard <| (repr (0 : Multiset (List ℕ)) |>.pretty 15) = "0" unsafe guard <| (repr ({[1, 2, 3], [4, 5, 6]} : Multiset (List ℕ)) |>.pretty 15) = "{[1, 2, 3],\n [4, 5, 6]}" unsafe guard <| (repr (∅ : Finset (List ℕ)) |>.pret...
TacticAnalysis.lean
/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Batteries.Data.Array.Merge import Lean.Elab.Tactic.Meta import Lean.Util.Heartbeats import Lean.Server.InfoUtils import Mathlib.Lean.ContextInfo /-! # Tactic ana...
Generalize.lean
/- Copyright (c) 2024 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init import Lean.Elab.Binders import Lean.Elab.Tactic.ElabTerm import Lean.Meta.Tactic.Generalize /-! # Backwards compatibility shim for `generalize`. I...
Trifunctor.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.GradedObject.Bifunctor import Mathlib.CategoryTheory.Functor.Trifunctor /-! # The action of trifunctors on graded objects Given a trifunctor `F. ...
Finset.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.Algebra.BigOperators.Group.Finset.Pi import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise import Mathlib.Algebra.BigOperators.GroupWithZero.Finse...
mk_all.lean
/- Copyright (c) 2024 Yaël Dillies, Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Damiano Testa -/ import Cli.Basic import Lake.CLI.Main import Mathlib.Util.GetAllModules -- The `style.header` linter flags `import Lake.CLI.Main` as a pote...
Compare.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.RingTheory.WittVector.Truncated import Mathlib.RingTheory.WittVector.Identities import Mathlib.NumberTheory.Padics.RingHoms /-! # Co...
Tangent.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Geometry.Manifold.VectorBundle.Basic /-! # Tangent bundles This file defines the tangent bundle as a `C^n` vector bundle. Let `...
Basic.lean
/- Copyright (c) 2024 Anatole Dedeker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedeker, Etienne Marion, Florestan Martin-Baillon, Vincent Guirardel -/ import Mathlib.Topology.Algebra.MulAction import Mathlib.Topology.Maps.Proper.Basic import Mathlib.Topo...
RingSeminorm.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, Yaël Dillies -/ import Mathlib.Algebra.Order.Ring.IsNonarchimedean import Mathlib.Analysis.Normed.Field.Lemmas import Mathlib.Analysis.S...
LocallyCompact.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.Lemmas import Mathlib.Analysis.Normed.Field.ProperSpace import Mathlib.RingTheory.DiscreteValuationRing.Basic import Mathlib.Ri...
Hom.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.Tactic.StacksAttribute import Mathlib.Topology.ContinuousMap.Basic import Mathlib.Topology.Maps.Proper.Basic /-! # Spectral maps This file defines spectr...
End.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.Equiv.Opposite import Mathlib.Algebra....
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
PostTuringMachine.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.Computability.Tape import Mathlib.Data.Finset.Prod import Mathlib.Data.Finset.Option import Mathlib.Data.Fintype.Defs import Mathlib.Data.PFun /-! # T...
Field.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.Algebra.Field.Defs import Mathlib.Algebra.Order.Positive.Ring /-! # Algebraic structures on the set of positive numbers In this file we prove that ...
classfun.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
Check.lean
/- Copyright (c) 2024 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.Elab.Tactic.Basic import Lean.PrettyPrinter import Lean.Elab.SyntheticMVars /-! # `#check` tactic This module defines a tactic version of ...
Skyscraper.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Junyan Xu -/ import Mathlib.Topology.Sheaves.PUnit import Mathlib.Topology.Sheaves.Stalks import Mathlib.Topology.Sheaves.Functors /-! # Skyscraper (pre)sheaves A skyscra...
UnitTrinomial.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Algebra.Polynomial.Mirror import Mathlib.Algebra.Ring.Regular import Mathlib.Data.Int.Order.Units import Mathlib.RingTheory.Coprime.Basic /-! # Unit...
HasConicalTerminal.lean
/- Copyright (c) 2025 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Jon Eugster, Emily Riehl -/ import Mathlib.CategoryTheory.Enriched.Limits.HasConicalProducts /-! # Existence of conical terminal objects -/ universe w v' v u u' names...
FreeAlgebra.lean
/- Copyright (c) 2020 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Adam Topaz, Eric Wieser -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.FreeMonoid.UniqueProds imp...
MonCat.lean
import Mathlib.Algebra.Category.MonCat.Basic -- We verify that the coercions of morphisms to functions work correctly: example {R S : MonCat} (f : R ⟶ S) : ↑R → ↑S := f -- It's essential that simp lemmas for `→*` apply to morphisms. example {R S : MonCat} (i : R ⟶ S) (r : R) (h : r = 1) : i r = 1 := by simp [h] exam...
Oplax.lean
/- Copyright (c) 2022 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.CategoryTheory.Bicategory.Modification.Oplax /-! # The bicategory of oplax functors between two bicategories Given bicategories `B` and `C`, we give a bica...
TrailingDegree.lean
/- Copyright (c) 2020 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Polynomial.Degree.Support import Mathlib.Data.ENat.Basic /-! # Trailing degree of univariate polynomials ## Main definitions * `trailingDegree...
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...
AlgebraicClosure.lean
/- Copyright (c) 2024 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu, Jiedong Jiang -/ import Mathlib.FieldTheory.Normal.Closure import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.FieldTheory.IntermediateField.Algebraic /-! # Relative...
List.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.Logic.Small.Basic import Mathlib.Data.Vector.Basic /-! # Instances for `Small (List α)` and `Small (Vector α)`. These must not be in `Logic.Small.Basic` ...
Group.lean
/- Copyright (c) 2025 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual import Mathlib.Order.CompleteLattice.Basic /-! # Complete l...
FDeriv.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.FDeriv.Equiv import Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn /-! # Inverse functio...
Real.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Geometry.Manifold.IsManifold.Basic import Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary import Mathlib.Analysis.InnerProductSpace.PiL2 /...
Sub.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import Mathlib.MeasureTheory.Integral.Lebesgue.Add /-! # Subtraction of Lebesgue integrals In this file we first show that Lebesgue integrals can be...
TransferInstance.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.GroupWithZero.Action.TransferInstance import Mathlib.Algebra.Module.Equiv.Defs /-! # Transfer algebraic structures across `Equiv`s This conti...
Fin.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.LinearAlgebra.Alternating.Curry import Mathlib.GroupTheory.Perm.Fin import Mathlib.Data.Fin.Parity /-! # Uncurrying alternating maps Given a functi...
Extensive.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.EffectiveEpi.Preserves import Mathlib.CategoryTheory.EffectiveEpi.Coproduct import Mathlib.CategoryTheory.Extensive import Mathlib.C...
Whiskering.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Whiskering import Mathlib.CategoryTheory.Adjunction.Basic /-! Given categories `C D E`, functors `F : D ⥤ E` and `G : E ⥤ D` with an adjunctio...
OrderIsoNat.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.Nat.Lattice import Mathlib.Logic.Denumerable import Mathlib.Logic.Function.Iterate import Mathlib.Order.Hom.Basic import Mathlib.Data.Set.Subsing...
SubmonoidClosure.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.Order.Filter.AtTopBot.Group import Mathlib.Topology.Algebra.Group.Basic /-! # Topological closure of the submonoid closure In this file we prove s...
ContinuousMap.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.Topology.Metrizable.Uniformity import Mathlib.Topology.UniformSpace.CompactConvergence /-! # Metrizability of `C(X, Y)` If `X` is a weakly locally ...
Images.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.Grp.Abelian import Mathlib.CategoryTheory.Limits.Shapes.Images /-! # The category of commutative additive groups has images. Note that w...
Trace.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Antoine Labelle -/ import Mathlib.LinearAlgebra.Contraction import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff import Mathlib....
Extension.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Frédéric Dupuis -/ import Mathlib.Data.Real.Archimedean import Mathlib.Geometry.Convex.Cone.Basic import Mathlib.LinearAlgebra.LinearPMap /-! # Extension theorems W...