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Multiset.lean
/- Copyright (c) 2019 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.Multiset.Defs import Mathlib.Algebra.Order.BigOperators.Group.List import Mathlib.Algebra.Order.Group.Abs import Mathlib.Alg...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
Frontend.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Control.Basic import Mathlib.Tactic.Linarith.Verification import Mathlib.Tactic.Linarith.Preprocessing import Mathlib.Tactic.Linarith.Oracle.SimplexA...
test_intro_rw.v
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Lemma test_dup1 : forall n : nat, odd n. Proof. move=> /[dup] m n; suff: odd n by []. Abort. Lemma test_dup2 : let n := 1 in False. Proof. move=> /[dup] m n; have : m = n :=...
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 Batteries.Data.String.Lemmas import Mathlib.Data.List.Lex import Mathlib.Data.Char import Mathlib.Algebra.Order.Group.Nat /-! # Strings Supplementary theorem...
Integral.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis, Anatole Dedecker -/ import Mathlib.Analysis.Normed.Algebra.Spectrum import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital import Mathlib.Analysis....
Instances.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.LocalRing.ResidueField.Ideal import Mathlib.FieldTheory.Separable /-! # Instances on residue fields -/ variable {R A B : Type*} [CommRing R] [Co...
MaxPowDiv.lean
/- Copyright (c) 2023 Matthew Robert Ballard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Matthew Robert Ballard -/ import Mathlib.Algebra.Divisibility.Units import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Tactic.Common /-! # The maximal power of one natural n...
Hom.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Amelia Livingston, Yury Kudryashov, Neil Strickland, Aaron Anderson -/ import Mathlib.Algebra.Divisibility.Basic import Mathlib.Algeb...
Functors.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves import Mathlib.Condensed.Light.Basic /-! # Functors from categories of topological spaces to light c...
Compact.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.LocallyConvex.Bounded import Mathlib.Topology.Algebra.Module.StrongTopology /-! # Compact operators In this file we define compact linea...
PFilter.lean
/- Copyright (c) 2020 Mathieu Guay-Paquet. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mathieu Guay-Paquet -/ import Mathlib.Order.Ideal /-! # Order filters ## Main definitions Throughout this file, `P` is at least a preorder, but some sections require more struc...
ProperSpace.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.MetricSpace.Pseudo.Basic import Mathlib.Topology.MetricSpace.Pseudo.Lemmas import Mathlib.Topology.MetricSpace.Pseudo.Pi import Mathlib...
HomogeneousLocalization.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Eric Wieser -/ import Mathlib.Algebra.Group.Submonoid.Finsupp import Mathlib.Order.Filter.AtTopBot.Defs import Mathlib.RingTheory.Adjoin.Basic import Mathlib.RingTheory.Gra...
PrincipalIdealDomain.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Morenikeji Neri -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.Algebra.EuclideanDomain.Field import Mathlib.Algebra.GCDMonoid.Basic import Mathlib.RingTheor...
Int.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Topology.Instances.Int /-! # ℤ as a normed group -/ open NNReal variable {...
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...
SheafComparison.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.Sites.Coherent.Comparison import Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves import Mathlib.CategoryTheory.Sites.Coherent...
LpEquiv.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.Normed.Lp.PiLp import Mathlib.Analysis.Normed.Lp.lpSpace import Mathlib.Topology.ContinuousMap.Bounded.Normed /-! # Equivalences among $L^p$ sp...
RenameBVar.lean
/- Copyright (c) 2019 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Patrick Massot -/ import Lean.Elab.Tactic.Location import Mathlib.Util.Tactic import Mathlib.Lean.Expr.Basic /-! # The `rename_bvar` tactic This file defines the `re...
IsLocallyClosed.lean
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.Topology.Order.OrderClosed import Mathlib.Topology.LocallyClosed /-! # Intervals are locally closed We prove that the intervals on a topological ordere...
Matrix.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Eric Wieser -/ import Mathlib.Topology.Algebra.InfiniteSum.Basic import Mathlib.Topology.Algebra.Ring.Basic import Mathlib.Topology.Algebra.Star import Mathlib.LinearAlgebra....
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
Valuation.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.RingTheory.HahnSeries.Multiplication import Mathlib.RingTheory.Valuation.Basic /-! # Valuations on Hahn Series rings If `Γ` is a `LinearOrderedCancelA...
GuardGoalNums.lean
import Mathlib.Tactic.GuardGoalNums set_option linter.unusedTactic false example : true ∧ true := by constructor guard_goal_nums 2 all_goals {constructor} example : (true ∧ true) ∧ (true ∧ true) := by constructor <;> constructor guard_goal_nums 4 all_goals {constructor}
LocallyFinite.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.LocallyFinite import Mathlib.Topology.Compactness.Compact /-! # Compact sets and compact spaces and locally finite functions -/ open Set ...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
PullbackContinuous.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback import Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafification import Mathlib.Algebra.Category.ModuleCat.Sheaf.Pu...
Basic.lean
/- Copyright (c) 2015 Nathaniel Thomas. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Group.Submonoid.BigOperators import Mathlib.Algebra.Module...
Uniform.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Continuity import Mathlib.Topology.Algebra.IsUniformGroup.Basic import Mathlib.Topology.MetricSpace...
Contraction.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation import Mathlib.LinearAlgebra.CliffordAlgebra.Fold import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic import Mathlib...
DirectoryDependency.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 Lean.Elab.Command import Lean.Elab.ParseImportsFast /-! # The `directoryDependency` linter The `directoryDependency` linter detects imports between directories t...
Normalize.lean
import Mathlib.Tactic.CategoryTheory.Bicategory.Normalize open CategoryTheory Mathlib.Tactic BicategoryLike open Bicategory namespace CategoryTheory.Bicategory /-- `normalize% η` is the normalization of the 2-morphism `η`. 1. The normalized 2-morphism is of the form `α₀ ≫ η₀ ≫ α₁ ≫ η₁ ≫ ... αₘ ≫ ηₘ ≫ αₘ₊₁` where e...
Basic.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Analysis.Normed.Group.Constructions import Mathlib.Analysis.Normed.Group.Subgroup impor...
Main.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import ImportGraph.CurrentModule import ImportGraph.Imports import Mathlib.Data.String.Defs import Mathlib.Util.FormatTable import Cli import LongestPole.SpeedCenterJson ...
Basic.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Reid Barton, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Connected import Mathlib.CategoryTheory.Limits.Constructions.Over.Products import Mathlib.CategoryTheo...
SelectInsertParamsClass.lean
/- Copyright (c) 2023 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Init import Lean.Widget.InteractiveGoal import Lean.Elab.Deriving.Basic /-! # SelectInsertParamsClass Defines the basic class of parameters for a sel...
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...
OrderDual.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.Group.Synonym import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual import Mathlib.Alg...
Semiconj.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone -/ import Mathlib.Dynamics.TopologicalEntropy.CoverEntropy /-! # Topological entropy of the image of a set under a semiconjugacy Consider two dynamica...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
NatCount.lean
/- Copyright (c) 2021 Vladimir Goryachev. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vladimir Goryachev -/ import Mathlib.Data.Nat.Count import Mathlib.Data.Set.Card /-! # Counting on ℕ This file provides lemmas about the relation of `Nat.count` with cardinality...
fail_if_no_progress.lean
import Mathlib.Tactic.FailIfNoProgress import Mathlib.Tactic.Basic set_option linter.unusedVariables false set_option linter.style.setOption false set_option pp.unicode.fun true section success example : 1 = 1 := by fail_if_no_progress rfl example (h : 1 = 1) : True := by fail_if_no_progress simp at h trivial e...
Subperm.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Batteries.Data.List.Perm import Mathlib.Data.List.Basic /-! # List Sub-permutations This file develops theory about ...
ssrbool.v
From mathcomp Require Import ssreflect ssrfun. From Corelib Require Export ssrbool. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. (**********************) (* not yet backported *) (**********************) Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT] [aP : pred ...
SimpleFuncDenseLp.lean
/- Copyright (c) 2022 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Heather Macbeth -/ import Mathlib.MeasureTheory.Function.L1Space.AEEqFun import Mathlib.MeasureTheory.Function.LpSpace.Complete import Mathlib.MeasureThe...
Pointwise.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.Functor.KanExtension.Basic /-! # Pointwise Kan extensions In this file, we define the notion of pointwise (left) Kan extension. Given two functo...
Prod.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Group.Prod import Mathlib.Data.Nat.Cast.Defs /-! # The product of two `AddMonoidWithOne`s. -/ assert_not_exists MonoidWithZero variable {α β...
MinimalAxioms.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.Algebra.Ring.Defs import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.MinimalAxioms /-! # Minimal Axioms for a Ring This file defines constr...
KernelPair.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.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryTheory.Limits.Shapes.RegularMono...
separable.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...
pgroup.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import fintype bigop finset prime fingroup morphism. From mat...
Defs.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, Kevin Buzzard, Yury Kudryashov -/ import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.Algebra.Module.Submodule.Defs import Mathlib.GroupTheory.Quoti...
Taylor.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.Algebra.EuclideanDomain.Field import Mathlib.Algebra.Polynomial.Module.Basic import Mathlib.Analysis.Calculus.Co...
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...
Normalizer.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.Abelian import Mathlib.Algebra.Lie.IdealOperations import Mathlib.Algebra.Lie.Quotient /-! # The normalizer of Lie submodules and subalgebras. ...
GammaDeriv.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.Convex.Deriv import Mathlib.Analysis.SpecialFunctions.Gamma.Deligne import Mathlib.Data.Nat.Factorial.Basic import Mathlib.NumberTheory.Harmo...
Periodic.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Nicolò Cavalleri -/ import Mathlib.Algebra.Ring.Periodic import Mathlib.Topology.ContinuousMap.Algebra /-! # Sums of translates of a continuous function is a period contin...
Finite.lean
/- Copyright (c) 2025 Yaël Dillies, Patrick Luo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Patrick Luo -/ import Mathlib.GroupTheory.Finiteness import Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup /-! # Localization of a finitely generate...
separable.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...
vcharacter.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...
Basic.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Mario Carneiro -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Group.End import Mathlib.Logic.Equiv.Set import Mathlib.Tactic.Common /-! #...
Character.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.Lie.Abelian import Mathlib.Algebra.Lie.Solvable import Mathlib.LinearAlgebra.Dual.Defs /-! # Characters of Lie algebras A character of a Lie algebr...
NoncommProd.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Algebra.Group.Commute.Hom import Mathlib.Algebra.Group.Pi.Lemmas import Mathlib.Data.Fintype.B...
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...
Lifts.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Eval.Subring import Mathlib.Algebra.Polynomial.Monic /-! # Polynomials that lift Gi...
Ideal.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.Algebra.MonoidAlgebra.Ideal import Mathlib.Algebra.MvPolynomial.Division /-! # Lemmas about ideals of `MvPolynomial` Notably this contains results about mo...
Core.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.Tactic.Attr.Register /-! # Simp tags for core lemmas In Lean 4, an attribute declared with `register_simp_attr` cannot be used in the same file. So...
Tendsto.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad -/ import Mathlib.Order.Filter.Basic import Mathlib.Order.Filter.Map /-! # Convergence in terms of filters The general notion of limit of a map with res...
seq.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. (******************************************************...
SumCoeff.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.Analysis.Asymptotics.SpecificAsymptotics import Mathlib.Analysis.InnerProductSpace.Calculus import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals im...
SplitEqualizer.lean
/- Copyright (c) 2024 Jack McKoen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jack McKoen -/ import Mathlib.CategoryTheory.Limits.Shapes.Equalizers /-! # Split Equalizers We define what it means for a triple of morphisms `f g : X ⟶ Y`, `ι : W ⟶ X` to be a split e...
Chunk.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Combinatorics.SimpleGraph.Regularity.Bound import Mathlib.Combinatorics.SimpleGraph.Regularity.Equitabilise import Mathlib.Comb...
StarOrdered.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Order.Star.Basic import Mathlib.Topology.ContinuousMap.ContinuousMapZero import Mathlib.Topology.ContinuousMap.Ordered /-! # Continuous function...
numdomain.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...
OfBilinear.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.LinearAlgebra.RootSystem.Defs /-! # Root pairings made from bilinear forms A common construction of root systems is given by taking the set of all vec...
LeftDerived.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.KanExtension.Basic import Mathlib.CategoryTheory.Localization.Predicate /-! # Left derived functors In this file, given a functor `F : C...
Ideal.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.RingTheory.Ideal.Operations import Mathlib.RingTheory.UniqueFactorizationDomain.Defs /-! # Unique factorization and as...
Imo2001Q3.lean
/- Copyright (c) 2025 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Data...
Deriv.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov, David Loeffler -/ import Mathlib.Analysis.Convex.Slope import Mathlib.Analysis.Calculus.Deriv.MeanValue /-! # Convexity of functions and derivat...
notation3.lean
import Mathlib.Util.Notation3 import Mathlib.Data.Nat.Basic set_option linter.style.setOption false set_option pp.unicode.fun true set_option autoImplicit true namespace Test -- set_option trace.notation3 true def Filter (α : Type) : Type := (α → Prop) → Prop def Filter.atTop [Preorder α] : Filter α := fun _ => Tru...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Basic.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.BigOperators.Finprod import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Mathlib.Algebra.NoZ...
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...
PreservesSheafification.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.Localization import Mathlib.CategoryTheory.Sites.CompatibleSheafification import Mathlib.CategoryTheory.Sites.Whiskering import Mathlib.Cate...
Interval.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.DFinsupp.Interval import Mathlib.Data.DFinsupp.Multiset import Mathlib.Order.Interval.Finset.Nat import Mathlib.Data.Nat.Lattice /-! # Finite intervals...
Defs.lean
/- Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Patrick Massot -/ -- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl. import Mathlib.Algebra.Group.Subgroup.Ker import...
Radical.lean
/- Copyright (c) 2024 Jineon Baek, Seewoo Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jineon Baek, Seewoo Lee, Bhavik Mehta, Arend Mellendijk -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.Algebra.Order.Group.Finset import Mathlib.RingTheory.Cop...
HomotopyEquivalence.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.DoldKan.Normalized /-! # The normalized Moore complex and the alternating face map complex are homotopy equivalent In this file, when the ca...
BestFirst.lean
import Mathlib.Data.MLList.BestFirst import Mathlib.Data.Nat.Basic /-! # Testing best first search and beam search. We check that `bestFirstSearch` can find its way around a wall. -/ open Lean MLList Function def Point := Int × Int deriving Repr def wall : Point → Bool := fun ⟨x, y⟩ => x ≤ 3 || y ≤ 3 || x ≥ 20 |...
Basic.lean
/- Copyright (c) 2015 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis -/ import Mathlib.Algebra.Group.Torsion import Mathlib.Algebra.Order.Group.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Algebra...
Semisimple.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Module.Torsion import Mathlib.FieldTheory.Perfect import Mathlib.LinearAlgebra.AnnihilatingPolynomial import Mathlib.RingTheory.Artinian.Instances im...
nilpotent.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 div bigop prime finset fingroup morphism. Fro...
Module.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Spectrum.Prime.Topology import Mathlib.RingTheory.Support /-! # Subsets of prime spectra related to modules ## Main results - `LocalizedModule...
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...
Complex.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex /-! # Lebesgue measure on `ℂ` In this fi...
MkIffOfInductive.lean
import Mathlib.Tactic.MkIffOfInductiveProp import Mathlib.Data.List.Perm.Lattice mk_iff_of_inductive_prop List.Chain test.chain_iff example {α : Type _} (R : α → α → Prop) (a : α) (al : List α) : List.Chain R a al ↔ al = List.nil ∨ ∃ (b : α) (l : List α), R a b ∧ List.Chain R b l ∧ al = b :: l := test.chai...
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. (**********************...
Lattice.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.Operations import Mathlib.Algebra.Algebra.Subalgebra.Basic /-! # Complete lattice structure of subalgebras In this file we def...