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EllipticDivisibilitySequence.lean
/- Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.Data.Nat.EvenOddRec import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination /-! # Elliptic divisibility sequences ...
binomial.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 div fintype tuple ...
Endomorphism.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Kim Morrison, Simon Hudon -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Opposite import Mathlib.Alg...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Data.Set.NAry import Mathlib.Data.ULift import Mathlib.Order.CompleteLattice.Defs import Mathlib.Order.Hom.Set /-! # Theory of complete lattices This...
tuple.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. From mathcomp Require Import seq choice fintype path. S...
End.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Group.Equiv.TypeTags import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Prod import Mathlib.Alg...
Units.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.Domain import Mathlib.Algebra.Polynomial.Degree.SmallDegree /-! # Degree of polyno...
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...
Kaehler.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.Etale.Basic import Mathlib.RingTheory.Kaehler.JacobiZariski import Mathlib.RingTheory.Localization.BaseChange import Mathlib.RingTheory.Smooth.Kae...
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.
SmoothTransition.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.Deriv.Inv import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathlib.Analysis.SpecialFunctions.ExpDeriv ...
MorphismProperty.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.AlgebraicTopology.SimplexCategory.Basic import Mathlib.CategoryTheory.MorphismProperty.Composition /-! # Properties of morphisms in the simplex category In thi...
Finite.lean
/- Copyright (c) 2020 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.Algebra.Group.Submonoid.BigOperators import Mathlib.Data.Finite.Card import Mathlib.Data.Set.Finite.Range /-! # ...
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...
Frm.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.Order.Category.Lat import Mathlib.Order.Hom.CompleteLattice import Mathlib.CategoryTheory.ConcreteCategory.Bundled /-! # The category of frames This file...
Basic.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.Analysis.Convex.Hull /-! # Convex cones In a `R`-module `M`, we define a convex cone as a set `s` such that `a • x + b • y ∈ s` wh...
Artinian.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu, Andrew Yang -/ import Mathlib.RingTheory.HopkinsLevitzki import Mathlib.RingTheory.Jacobson.Ring /-! # Artinian rings over jacobson rings ## Main results - `Module.finite_iff...
Metric.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Analysis.Normed.Group.Continuity import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic import Mathlib.Topology.MetricSpace.Thick...
ZeroAtInfty.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.Topology.ContinuousMap.Bounded.Star import Mathlib.Topology.ContinuousMap.CocompactMap /-! # Continuous functions vanishing at infinity The type of con...
Substitution.lean
/- Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María Inés de Frutos Fernández -/ import Mathlib.RingTheory.MvPowerSeries.Evaluation import Mathlib.RingTheory.MvPowerSer...
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 -/ import Mathlib.Algebra.Category.MonCat.Basic import Mathlib.Algebra.Group.End import Mathlib.CategoryTheory.Endomorphism import Mathlib.Data.Int.Cast.Lemmas /-! # Ca...
intdiv.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 div choice fintype...
Limits.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory import Mathlib.CategoryTheory.Monoidal.Limits.Basic import Mathlib.CategoryTheory.Limits.Preserves.Basic ...
SingleHomology.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.Algebra.Homology.Single import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex /-! # The homology of single complexes The main definition in this file ...
Basic.lean
/- Copyright (c) 2022 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.RingTheory.Ideal.BigOperators import Mathlib.RingTheory.Polynomial.Eisenstein.Criterion import Mathlib.RingTheory.Polynomial.ScaleRoots /-! # Eisens...
EvenEquiv.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.Even import Mathlib.LinearAlgebra.QuadraticForm.Prod /-! # Isomorphis...
Defs.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, Simon Hudon, Mario Carneiro -/ import Mathlib.Tactic.Lemma import Mathlib.Tactic.TypeStar import Mathlib.Tactic.ToAdditive import Mathlib.Util.AssertEx...
UnionLift.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Set.Lattice import Mathlib.Order.Directed /-! # Union lift This file defines `Set.iUnionLift` to glue together functions defined on each of a collect...
Submonoid.lean
/- Copyright (c) 2024 David Ang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Ang -/ import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.GroupTheory.GroupAction.Defs /-! # The subgroup of fixed points of an action -/ variable (M α : Type*) [Monoid...
Multigoal.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.Elab.Command -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstring. import Mathlib.Tactic.Linter.He...
Pairwise.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Finset.Lattice.Fold import Mathlib.Data.Set.Pairwise.List /-! # Relations holding pairwise on finite sets In this file we prove a few results about ...
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...
Order.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Anne Baanen -/ import Mathlib.Logic.Function.Iterate import Mathlib.Order.GaloisConnection.Basic import Mathlib.Order.Hom.Basic /-! # Lattice structure on order homomorph...
FilteredColimits.lean
/- Copyright (c) 2024 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Comma.Presheaf.Colimit import Mathlib.CategoryTheory.Limits.Filtered import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLim...
Motzkin.lean
/- Copyright (c) 2025 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan, Heather Macbeth -/ import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Positivity /-! # The Motzkin polynomial The Motzkin polynomial is a well-known counterexample...
AssertExists.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kim Morrison -/ import Mathlib.Init import Lean.Elab.Command import Mathlib.Util.AssertExistsExt /-! # User commands for assert the (non-)existence of declaration or ins...
commutator.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 fintype. From mathcomp Require Import bigop finset binomial fingroup morphism. From mathcomp...
Basic.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Judith Ludwig, Christian Merten -/ import Mathlib.Algebra.Ring.GeomSum import Mathlib.LinearAlgebra.SModEq import Mathlib.RingTheory.Jacobson.Ideal import Mathlib.RingTheory.Idea...
Symmetric.lean
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic deprecated_module (since := "2025-05-08")
Ring.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.NatAntidiagonal import Mathlib.Topology.Algebra.InfiniteSum.Constructions import Mathlib.Topology.Algebra.Ring.Basic /-! # Infini...
BoundedLattice.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.Order.Hom.Bounded import Mathlib.Order.Hom.Lattice import Mathlib.Order.SymmDiff /-! # Bounded lattice homomorphisms This file defines bounded lattice ho...
AddChar.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.DirectSum.Basic import Mathlib.Algebra.Group.AddChar /-! # Direct sum of additive characters This file defines the direct sum of additive charact...
Smeval.lean
/- Copyright (c) 2023 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Group.NatPowAssoc import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Eval.SMul /-! # Scalar-multiple polynomial ev...
finfield.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 div tupl...
CountableSeparatingOn.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.Order.Filter.CountableInter /-! # Filters with countable intersections and countable separating families In this file we prove some facts about a f...
SheafEquiv.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Sites.DenseSubsite.Basic /-! # The equivalence of categories of sheaves of a dense subsite - `CategoryTheory.Functor.IsDenseSubsite.sheafEq...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
PPRoundtrip.lean
import Mathlib.Tactic.Linter.PPRoundtrip /-- info: "a a" --- warning: source context 'al " a ' 'al " a a\n' pretty-printed context Note: This linter can be disabled with `set_option linter.ppRoundtrip false` -/ #guard_msgs in set_option linter.ppRoundtrip true in #eval " a a\n " |>.trim /-- warnin...
CompleteLattice.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, Yury Kudryashov, Patrick Massot -/ import Mathlib.Order.ConditionallyCompleteLattice.Indexed import Mathlib.Order.Filter.AtTopBot.Tendsto /-! # `Filter....
center.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 fingroup morphism perm. From math...
Imo1960Q1.lean
/- Copyright (c) 2020 Kevin Lacker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Lacker -/ import Mathlib.Data.Nat.Digits.Lemmas /-! # IMO 1960 Q1 Determine all three-digit numbers $N$ having the property that $N$ is divisible by 11, and $\dfrac{N}{11}$ is eq...
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 :=...
Ordered.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Shing Tak Lam -/ import Mathlib.Topology.Order.Lattice import Mathlib.Topology.Order.ProjIcc import Mathlib.Topology.ContinuousMap.Defs /-! # Bundled continuous maps into ...
DualLattice.lean
/- Copyright (c) 2018 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.LinearAlgebra.BilinearForm.Properties /-! # Dual submodule with respect to a bilinear form. ## Main definitions and results - `BilinForm.dualSubmodule`: T...
Order.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.Sym.Sym2 import Mathlib.Order.Lattice /-! # Sorting the elements of `Sym2` This files provides `Sym2.sortEquiv`, the forward direction of which is som...
WithZero.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johan Commelin -/ import Mathlib.Algebra.Group.TypeTags.Basic import Mathlib.Algebra.Group.WithOne.Defs import Mathlib.Algebra.GroupWithZero.Equiv import Mathlib.Algebr...
HasFiniteIntegral.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou -/ import Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable import Mathlib.MeasureTheory.Integral.Lebesgue.DominatedConvergence import Mathlib.Measure...
ClosedCompactCylinders.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Peter Pfaffelhuber -/ import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic import Mathlib.MeasureTheory.Constructions.Cylinders /-! # Cylinders with closed compact ...
Hahn.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Loic Simon -/ import Mathlib.MeasureTheory.Measure.Typeclasses.Finite /-! # Unsigned Hahn decomposition theorem This file proves the unsigned version of the Hahn deco...
PolynomialAlgebra.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.Polynomial.AlgebraMap import Mathlib.RingTheory.IsTensorProduct /-! # Base change of polynomial algebras Given `[CommSemiring R] [Semiring A] [Al...
WellFounded.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.DFinsupp.WellFounded import Mathlib.Data.Finsupp.Lex /-! # Well-foundedness of the lexicographic and product orders on `Finsupp` `Finsupp.Lex.wellFounded`...
Restrict.lean
/- Copyright (c) 2021 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Cover.Open import Mathlib.AlgebraicGeometry.Over /-! # Restriction of Schemes and Morphisms ## Main definition - `AlgebraicGeometry.Schem...
Multiplicity.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.Nat.Choose.Factorization /-! # Natural number multiplicity This file contains lemmas about the multiplicity function (the maximum prime power dividi...
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.
RuzsaCovering.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.Algebra.Group.Action.Pointwise.Finset import Mathlib.Data.Real.Basic import Mathlib.Order.Preorder.Finite import Mathlib.SetTheory.Cardinal.Finite import M...
eqtype.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. (********************************************************************...
Colimits.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.Sheafification /-! # Colimits in categories of sheaves of modules In this file, we show that colimits of shape `J` exist in...
RSuffices.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.Tactic.Basic /-! # `rsuffices` tactic The `rsuffices` tactic is an alternative version of `suffices`, that allows the usage of any syntax that would be val...
TopModuleCat.lean
import Mathlib.Algebra.Category.ModuleCat.Topology.Basic universe v u open CategoryTheory TopModuleCat set_option maxHeartbeats 10000 set_option synthInstance.maxHeartbeats 2000 variable (R : Type u) [CommRing R] [TopologicalSpace R] [IsTopologicalRing R] /- We test if all the coercions and `map_add` lemmas trigge...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
BinaryRec.lean
import Mathlib.Data.Nat.Bits def Nat.popcountTR (n : Nat) : Nat := n.binaryRec (·) (fun b _ f x ↦ f (x + b.toNat)) 0 /-- info: 1 -/ #guard_msgs in #eval Nat.popcountTR (2 ^ 20240)
EffectiveEpi.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.Topology.Category.CompHausLike.EffectiveEpi import Mathlib.Topology.Category.LightProfinite.Limits /-! # Effective epimorphisms in `LightProfinite...
Defs.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.Defs import Mathlib.Tactic.Abel /-! # Ideals over a ring This file defines `Ideal R`, the type of (left...
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...
Injective.lean
/- Copyright (c) 2023 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.Algebra.Module.Injective import Mathlib.CategoryTheory.Preadditive.Injective.Basic import Mathlib.Algebra.Category.ModuleCat.EpiMono /-! # Injective objec...
FunctorEquivalence.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.Algebra.Homology.ShortComplex.Basic /-! # Short complexes in functor categories In this file, it is shown that if `J` and `C` are two categories (such that `C`...
NormedSpace.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.Analysis.RCLike.Basic import Mathlib.Dynamics.BirkhoffSum.Average /-! # Birkhoff average in a normed space In this file we prove some lemmas about ...
Finite.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, Yury Kudryashov, Patrick Massot -/ import Mathlib.Data.Set.Finite.Lemmas import Mathlib.Order.Filter.Bases.Finite import Mathlib.Order.Filter.AtTopBot.Ba...
AEEqOfIntegral.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.InnerProductSpace.Continuous import Mathlib.MeasureTheory.Function.AEEqOfLIntegral import Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp imp...
Defs.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.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Algebra.Or...
Permanent.lean
/- Copyright (c) 2024 Moritz Firsching. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Firsching -/ import Mathlib.Data.Fintype.Perm import Mathlib.Data.Matrix.RowCol /-! # Permanent of a matrix This file defines the permanent of a matrix, `Matrix.permanent`, a...
Basic.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Asymptotics.Lemmas import Mathlib.Analysis.Calculus.FDeriv.Defs import Mathlib.Analysis.Calculus.TangentCone...
Finite.lean
/- Copyright (c) 2021 Henry Swanson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henry Swanson -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Combinatorics.Derangements.Basic import Mathlib.Data.Fintype.BigOperators import Mathlib.Tactic.Ring /-!...
CommSq.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.ShortComplex.Basic import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryTheory.Preadditive.Biproducts /-! # Relat...
Veblen.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.Ordinal.FixedPoint /-! # Veblen hierarchy We define the two-arguments Veblen function, which satisfies `veblen 0 a ...
Defs.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, Yaël Dillies, Yuyang Zhao -/ import Mathlib.Algebra.Order.Ring.Unbundled.Basic import Mathlib.Algebra.CharZero.Defs import Mathlib.Alge...
Prod.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot, Yury Kudryashov -/ import Mathlib.Util.AssertExists import Mathlib.Algebra.Notation.Defs import Mathlib.Data.Prod.Basic /-! # Arithmetic operators on (pa...
rat.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 prime fintype fi...
Integral.lean
/- Copyright (c) 2022 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Analysis.SpecialFunctions.Integrals.Basic import Mathlib.MeasureTheory.Integral.Layercake /-! # The integral of the real power of a nonnegative function ...
bigop.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 fintype tuple ...
TotallyRealComplex.lean
/- Copyright (c) 2022 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification /-! # Totally real and totally complex number fields This file defines the type of t...
Conservative.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.Constructions.BorelSpace.Basic import Mathlib.Dynamics.Ergodic.MeasurePreserving import Mathlib.Combinatorics.Pigeonhole /-! # Conserv...
Action.lean
/- Copyright (c) 2025 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.Matrix.Mul import Mathlib.Algebra.Ring.Opposite /-! # Actions by matrices on vectors through `*ᵥ` and `ᵥ*`, cast as `Module`s This file provides the ...
Category.lean
/- Copyright (c) 2018 Michael Jendrusch. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Jendrusch, Kim Morrison, Bhavik Mehta, Jakob von Raumer -/ import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Functor.Trifunctor import Mathlib.CategoryTheo...
Complex.lean
import Mathlib.Data.Complex.Basic import Mathlib.Algebra.DualNumber open DualNumber /-- info: Real.ofCauchy (sorry /- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... -/) + Real.ofCauchy (sorry /- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... -/)*I -/ #guard_msgs in #eval (0 : ℂ) /-- info: Real.ofCauchy (sorry /- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
all_order.v
Require Export order.
Differentiation.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Covering.VitaliFamily import Mathlib.MeasureTheory.Function.AEMeasurableOrder import Mathlib.MeasureTheory.Integral.Average import ...
LeftExact.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.Sites.Limits import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit import Mathlib.CategoryTheory.Adhesive import Mathlib.Categ...
all_order.v
Require Export order.
ProdHom.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Group.Prod import Mathlib.Algebra.GroupWithZero.Commute import Mathlib.Algebra.GroupWithZero.Units.Lemmas import Mathlib.Algebra.GroupWithZer...