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(* (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. (******************************************************************************) (* ...
Basic.lean
/- Copyright (c) 2025 Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang -/ import Mathlib.Algebra.Category.AlgCat.Basic import Mathlib.Algebra.Category...
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 -/ import Mathlib.Algebra.Group.Action.Basic import Mathlib.Algebra.GroupWithZero.Action.End import Mathlib.Algebra.Ring.Hom.Defs /-! # Group action on rings This file defines t...
OrderedSMul.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.Invertible import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Order.Modu...
Hadamard.lean
/- Copyright (c) 2021 Lu-Ming Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lu-Ming Zhang -/ import Mathlib.LinearAlgebra.Matrix.Trace import Mathlib.Data.Matrix.Basic /-! # Hadamard product of matrices This file defines the Hadamard product `Matrix.hadamard`...
Hom.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 /-! # Morphisms of root pairings This file defines morphisms of root pairings, following the definition of morphisms of ...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
Simple.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.RingTheory.SimpleModule.Basic import Mathlib.Topology.Algebra.Module.Basic /-! # The kernel of a linear function is closed or dense In this file ...
MonicNonRegular.lean
/- Copyright (c) 2023 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Polynomial.Monic /-! # `Monic` does not necessarily imply `IsRegular` in a `Semiring` with no opposites This counterexample shows that the hyp...
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, Jeremy Avigad -/ import Mathlib.Order.Filter.Germ.OrderedMonoid import Mathlib.Algebra.Order.Ring.Defs /-! # Lemmas about filters and ordered rings. -/ namespace Filte...
Bousfield.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.ObjectProperty.ClosedUnderIsomorphisms import Mathlib.CategoryTheory.MorphismProperty.Composition import Mathlib.CategoryTheory.Localization.Adjun...
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...
LinearMapPiProd.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Topology.Algebra.Module.LinearMap /-! # Continuous linear maps ...
CoreM.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 Mathlib.Init /-! # Additional functions using `CoreM` state. -/ open Lean Core /-- Run a `CoreM α` in a fresh `Environment` with specified `modules : List Name`...
Sylow.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Thomas Browning -/ import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Data.SetLike.Fintype import Mathlib.GroupTheory.PGroup import Mathlib.GroupTheory.NoncommPi...
DFinsupp.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau -/ import Mathlib.Data.DFinsupp.Submonoid import Mathlib.Data.DFinsupp.Sigma import Mathlib.Data.Finsupp.ToDFinsupp import Mathlib.LinearAlgebra.Finsupp.SumProd im...
MonoidalComp.lean
import Mathlib.Tactic.CategoryTheory.MonoidalComp universe v u noncomputable section namespace CategoryTheory open scoped MonoidalCategory variable {C : Type u} [Category.{v} C] [MonoidalCategory C] example (X : C) : X ≅ (X ⊗ (𝟙_ C ⊗ 𝟙_ C)) := monoidalIso _ _ example (X1 X2 X3 X4 X5 X6 X7 X8 X9 : C) : (𝟙_...
HomotopyCategory.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.Algebra.Homology.Homotopy import Mathlib.Algebra.Homology.Linear import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy import Mathlib.CategoryTheory....
Unbundled.lean
/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.Data.Set.Defs import Mathlib.Tactic.ExtendDoc import Mathlib.Tactic.Lemma import Mathlib.Tactic.SplitIfs import Mathlib.Tactic.TypeStar /-! ...
Weierstrass.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.Analysis.SpecialFunctions.Bernstein import Mathlib.Topology.Algebra.Algebra import Mathlib.Topology.ContinuousMap.Compact /-! # The Weierstrass approximat...
LeftRightLim.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.Order.LeftRight import Mathlib.Topology.Order.Monotone /-! # Left and right limits We define the (strict) left and right limits of a f...
WeakOperatorTopology.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual /-! # The weak operator topology This file defi...
Integrable.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.L1Space.HasFiniteIntegral import Mathlib.MeasureTheory.Function.LpOrder import Mathlib.MeasureTheory.Function.StronglyMeasurable.L...
MaxPowDiv.lean
import Mathlib.NumberTheory.Padics.PadicVal.Basic /-- info: 100000 -/ #guard_msgs in /- Previously this would hang -/ #eval padicValNat 2 (2 ^ 100000)
OrderOfVanishing.lean
/- Copyright (c) 2025 Raphael Douglas Giles. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Raphael Douglas Giles -/ import Mathlib.RingTheory.KrullDimension.NonZeroDivisors import Mathlib.RingTheory.Length import Mathlib.RingTheory.HopkinsLevitzki /-! # Order of vani...
choice.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (**************************************************...
Sections.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.List.Forall2 /-! # List sections This file proves some stuff about `List.sections` (definition in `Data.List.Defs`). A section of a list of lists...
Cardinality.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.GroupTheory.MonoidLocalization.Basic import Mathlib.GroupTheory.OreLocalization.Cardinality /-! # Cardinality of localizations of commutative monoids This file cont...
ComputeDegree.lean
import Mathlib.Tactic.ComputeDegree open Polynomial variable {R : Type*} section native_mathlib4_tests variable {n : ℕ} {z : ℤ} {f : ℤ[X]} (hn : natDegree f ≤ 5) (hd : degree f ≤ 5) /-- Flows through all the matches in `compute_degree`, with a `natDegree _ ≤ _` goal. -/ example : natDegree (- C z * X ^ 5 + (monom...
Unitor.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.GradedObject.Associator import Mathlib.CategoryTheory.GradedObject.Single /-! # The left and right unitors Given a bifunctor `F : C ⥤ D ⥤ D`, an ...
Basic.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fangming Li, Jujian Zhang -/ import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Algebra.Polynomial.Basic import Mathlib.Order.KrullDimension import Mathlib.RingTheory.Ideal.Quot...
EventuallyMeasurable.lean
/- Copyright (c) 2024 Felix Weilacher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Felix Weilacher -/ import Mathlib.MeasureTheory.MeasurableSpace.Defs import Mathlib.Order.Filter.CountableInter /-! # Measurability modulo a filter In this file we consider the gen...
Modular.lean
/- Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu -/ import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction import Mathlib.LinearAlgebra.Genera...
Units.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Tactic.Tauto import Mathlib.Algebra.Group.Int.Defs import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Nat.Units /-! # Units in the integers...
RestrictScalars.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.Tower /-! # The `RestrictScalars` type alias See the documentation attached to the `RestrictScalars` definition for advice on...
EulerSineProd.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Integrals.Basic import Mathlib.MeasureTheory.Integral.PeakFunction /-! # Euler's infinite product for the sine function Thi...
Killing.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.Lie.Derivation.Killing import Mathlib.Algebra.Lie.Killing import Mathlib.Algebra.Lie.Sl2 import Mathlib.Algebra.Lie.Weights.Chain import Mathlib.Line...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
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, Kevin Buzzard, Kim Morrison, Johan Commelin, Chris Hughes, Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Hom.Defs...
Epi.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Category.Ring.Basic import Mathlib.RingTheory.TensorProduct.Finite import Mathlib.CategoryTheory.ConcreteCategory.EpiMono /-! # Epimorphisms in `Com...
Colimits.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Reid Barton, Joël Riou -/ import Mathlib.Logic.UnivLE import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Limits.Types.ColimitType /-! # Colimits ...
Matrix.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition import Mathlib.LinearAlgebra.Dimension.Finite /-! # Finite and free modules using matrices We provide ...
Basic.lean
/- Copyright (c) 2025 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.SetLike.Basic import Mathlib.Order.SupIndep /-! # Partitions A `Partition` of an element `a` in a complete lattice is an independent family of nontr...
CompatiblePlus.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.Whiskering import Mathlib.CategoryTheory.Sites.Plus /-! In this file, we prove that the plus functor is compatible with functors which p...
Defs.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov -/ import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Algebra.Group.Subse...
Defs.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.MeasureTheory.Measure.GiryMonad /-! # Markov Kernels A kernel from a measurable space `α` to another measurable space `β` is a measurable map `α → Measur...
Equalizers.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Markus Himmel -/ import Mathlib.CategoryTheory.EpiMono import Mathlib.CategoryTheory.Limits.HasLimits /-! # Equalizers and coequalizers This file defines (co)equalizers a...
DayConvolution.lean
/- Copyright (c) 2025 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Monoidal.ExternalProduct.KanExtension import Mathlib.CategoryTheory.Products.Associator /-! # Day convolution monoidal structure Given f...
Canonical.lean
/- Copyright (c) 2014 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn -/ import Mathlib.Algebra.Order.Field.Defs import Mathlib.Algebra.Order.GroupWithZero.Canonical import Mathlib.Alg...
all_ssreflect.v
Attributes deprecated(since="mathcomp 2.5.0", note="Use 'all_boot' and/or 'all_order' instead."). From mathcomp Require Export all_boot. From mathcomp Require Export preorder. From mathcomp Require Export order.
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.
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 ...
Sym.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.List.Sym /-! # Unordered tuples of elements of a multiset Defines `Multiset.sym` and the specialized `Multiset.sym2` for computing multisets of all un...
poly.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
Indicator.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.Basic import Mathlib.Algebra.Group.Indicator import Mathlib.Order.CompleteLattice.Finset /-! # Interaction of big op...
poly.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
Yoneda.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.Algebra.Category.ModuleCat.Basic import Mathlib.CategoryTheory.Linear.Basic import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic /-! # The Yoneda embedd...
Contrapose.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.Tactic.Push /-! # Contrapose The `contrapose` tactic transforms the goal into its contrapositive when that goal is an implication. * `contrapose` ...
Dual.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.DFinsupp import Mathlib.LinearAlgebra.Dual.Basis import Mathlib.LinearAlgebra.Matrix.ToLin /-!...
ssreflect.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Export ssreflect. Global Set SsrOldRewriteGoalsOrder. Global Set Asymmetric Patterns. Global Set Bullet Behavior "None". #[deprecated(sinc...
Summable.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Analysis.Complex.UpperHalfPlane.Topology import Mathlib.Analysis.PSeries import Mathlib.Order.Interval.Finset.Box import Mathlib.Analysis.Asymptotics....
PID.lean
/- Copyright (c) 2023 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.DedekindDomain.Dvr import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas /-! # Criteria under which a Dedekind domain is a PID This file contain...
NormTrace.lean
/- Copyright (c) 2023 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Norm.Defs import Mathlib.RingTheory.Trace.Defs /-! # Relation between norms and traces -/ open Module lemma Algebra.norm_one_add_smul {A B} [Co...
OrderEmbedding.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.Interval.Set.UnorderedInterval import Mathlib.Order.Hom.Basic /-! # Preimages of intervals under order embeddings In this file we prove that ...
Notation.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.MeasureTheory.Function.ConditionalExpectation.Basic import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue /-! # Notations for probability theory Th...
Pi.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.Topology.MetricSpace.Pseudo.Pi import Mathlib.Topology.MetricSpace.Ultra.Basic /-! # Ultrametric distances on pi types This file contains results o...
TopologicallyNilpotent.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.Topology.Algebra.LinearTopology import Mathlib.RingTheory.Ideal.Basic imp...
Grp.lean
import Mathlib.Algebra.Category.Grp.Basic universe v u open CategoryTheory Grp set_option maxHeartbeats 10000 set_option synthInstance.maxHeartbeats 2000 /- We test if all the coercions and `map_add` lemmas trigger correctly. -/ example (X : Type u) [Group X] : ⇑(𝟙 (of X)) = id := by simp example {X Y : Type u} ...
Imo2005Q3.lean
/- Copyright (c) 2021 Manuel Candales. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Manuel Candales -/ import Mathlib.Data.Real.Basic import Mathlib.Tactic.Positivity import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.Ring /-! # IMO...
Defs.lean
/- Copyright (c) 2022 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Data.Set.CoeSort import Mathlib.Logic.Equiv.Defs import Mathlib.Tactic.Set import Mathlib.Util.AssertExists /-! # Definition of the `Finite` typeclass This...
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 ...
ssrmatching.v
From Corelib Require Export ssrmatching.
Equalizer.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.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Subpresheaf.Image /-! # The equalizer of two morphisms of presheaves, as a subpresheaf If...
Additive.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.Analysis.BoxIntegral.Partition.Split import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul /-! # Box additive functions We say that a function `f : ...
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 ...
IndicatorFunction.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov -/ import Mathlib.Algebra.Order.Group.Indicator import Mathlib.Algebra.Order.Pi import Mathlib.Analysis.Normed.Group.Basic /-! # Indicator function and (...
ShrinkingLemma.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.EMetricSpace.Paracompact import Mathlib.Topology.MetricSpace.Basic import Mathlib.Topology.MetricSpace.ProperSpace.Lemmas import Mathlib.Top...
Basic.lean
/- Copyright (c) 2020 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Jujian Zhang -/ import Mathlib.Algebra.Polynomial.DenomsClearable import Mathlib.Analysis.Calculus.MeanValue import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathl...
DefEqTransformations.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Tactic.Basic /-! # Tactics that transform types into definitionally equal types This module defines a standard wrapper that can be used to create tactics t...
Doubling.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.Analysis.SpecialFunctions.Log.Base import Mathlib.MeasureTheory.Measure.MeasureSpaceDef /-! # Uniformly locally doubling measures A uniformly locally doubl...
Constructions.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Data.Finset.Update import Mathlib.Data.Prod.TProd import Mathlib.Data.Set.UnionLift import Mathlib.GroupTheory.Coset.Defs import Mathli...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Basic.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Category.BialgCat.Basic import Mathlib.RingTheory.HopfAlgebra.Basic /-! # The category of Hopf algebras over a commutative ring We intr...
Inverse.lean
/- Copyright (c) 2020 Kenji Nakagawa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio -/ import Mathlib.RingTheory.FractionalIdeal.Operations /-! # Inverse operator for fractional ideals This file defines the notation ...
Bounded.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.MetricSpace.Bounded import Mathlib.Order.Filter.Pointwise /-! #...
Preserves.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Preadditive.Projective.Basic /-! # Preservation of projective objects We define a typeclass `Functor.PreservesProjectiveObjects`. We re...
Pi.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique import Mathlib.Algebra.Algebra.Spectrum.Pi import Mathlib.Algebra.Star.StarAlgHom /-! # T...
Integers.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.RingTheory.Valuation.Basic /-! # Ring of integers under a given valuation The elements with valuation less than or equal to 1. TODO: Define characteristic pre...
rewrites.lean
import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Nat.Prime.Defs import Mathlib.CategoryTheory.Category.Basic import Mathlib.Data.List.InsertIdx import Mathlib.Algebra.Group.Basic -- This is partially duplicative with the tests for `rw?` in Lean. -- It's useful to re-test here with a larger environment. private axi...
Basic.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.Group.Action.Opposite import Mathlib.Algebra.Group.Action.Units import Mathlib.Algebra.Group.Invertible.Defs import Mathlib.Algebra.GroupWithZero.U...
InteriorBoundary.lean
/- Copyright (c) 2023 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Mathlib.Geometry.Manifold.IsManifold.ExtChartAt /-! # Interior and boundary of a manifold Define the interior and boundary of a manifold. ## Main defini...
LinearIndependent.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.LinearAlgebra.LinearIndependent.Defs import Mathlib.RingTheory.Algebraic.Defs /-! # Linear independence of transcendental elements ## Main result * ...
InitTail.lean
/- Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. 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.Basic import Mathlib.RingTheory.WittVector.IsPoly /-! # `init` and `tail` Given a Witt vecto...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
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...
hint.lean
import Mathlib.Data.ENNReal.Basic import Mathlib.Data.Nat.Prime.Defs import Mathlib.Tactic.Common import Mathlib.Tactic.ComputeDegree import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Finiteness import Mathlib.Tactic.Linarith import Mathlib.Tactic.TautoSet /-- info: Try these: • linarith -/ #guard_msgs in example ...
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 :=...
Funext.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.Polynomial.RingDivision import Mathlib.Algebra.Polynomial.Roots import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Algebra.MvPolynomia...
Support.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Aaron Anderson, Yakov Pechersky -/ import Mathlib.Data.Fintype.Card import Mathlib.Algebra.Group.Commute.Basic import Mathlib.Algebra.Group.End import Mathlib.Data.Finset.N...
primitive_action.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. From mathcomp Require Import div seq fintype tuple finset. From mathcomp Require Import fin...