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TypeTags.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.Defs import Mathlib.Algebra.Order.Monoid.TypeTags import Mathlib.Tactic.Linter.Dep...
SubmoduleQuotient.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.LinearAlgebra.Quotient.Defs import Mathlib.MeasureTheory.MeasurableSpace.Constructions /-! # Measurability on the quotient of a module by a submodule -/ ...
Synonym.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.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.Order.GroupWithZero.Synonym import Mathlib.Tactic.Common /-! # Actions by and on order synonyms ...
JointEigenspace.lean
/- Copyright (c) 2024 Jon Bannon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Bannon, Jack Cheverton, Samyak Dhar Tuladhar -/ import Mathlib.Analysis.InnerProductSpace.Spectrum import Mathlib.LinearAlgebra.Eigenspace.Pi import Mathlib.LinearAlgebra.Eigenspace.S...
all_order.v
Require Export order.
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
zmod.lean
import Mathlib.Data.ZMod.Defs -- A Mersenne exponent, chosen so the test below takes no more than a few seconds -- but should be enough to trigger a stack overflow from a non-tail-recursive implementation -- of exponentiation by repeated squaring. def k := 11213 def p := 2^k - 1 #adaptation_note /-- 2025-06-23 in the...
Algebra.lean
/- Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Judith Ludwig, Christian Merten -/ import Mathlib.Algebra.Module.Torsion import Mathlib.Algebra.Algebra.Pi import Mathlib.RingTheory.AdicCompletion.Basic /-! # Algebr...
TightNormed.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.MeasureTheory.Measure.Tight import Mathlib.Order.CompletePartialOrder /-! # Tight sets of measures in norme...
Linear.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.Additive import Mathlib.CategoryTheory.Linear.LinearFunctor /-! # The category of homological complexes is linear In this file, we define the ...
CPolynomialDef.lean
/- Copyright (c) 2023 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.Analysis.Analytic.ChangeOrigin /-! We specialize the theory of analytic functions to the case of functions that admit a development given by a *finite* fo...
OfAddContent.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.SetSemiring import Mathlib.MeasureTheory.Measure.AddContent import Mathlib.MeasureTheory.Measure.Trim /-! # Carathéodory...
DyckWord.lean
/- Copyright (c) 2024 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Batteries.Data.List.Count import Mathlib.Combinatorics.Enumerative.Catalan import Mathlib.Tactic.Positivity /-! # Dyck words A Dyck word is a sequence consisting of ...
Equiv.lean
/- Copyright (c) 2025 Weiyi Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Weiyi Wang -/ import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Order.Group.Synonym /-! # Add/Mul equivalence for order type synonyms -/ variable (α : Type*) [Mul α] /-- `t...
burnside_app.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...
Hashing.lean
/- Copyright (c) 2023 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Jon Eugster -/ import Cache.IO import Lean.Elab.ParseImportsFast namespace Cache.Hashing open Lean IO open System hiding SearchPath /-- The `HashMemo` contains all ...
sylow.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 prime bigop finset fingroup morphism. From mat...
Basic.lean
/- Copyright (c) 2020 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Divisibility.Basic import Mathlib.Algebra.Group.Subgroup.Map import Mathlib.Algebra.Group.Int.Defs /-! # Subgroups generated by an element ## Tag...
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...
Rat.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Anne Baanen, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.Rat import Mathlib.Algebra.Module.LinearM...
VariableChange.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, David Kurniadi Angdinata, Jz Pan -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass /-! # Change of variables of Weierstrass curves This file defines admissible lin...
Instances.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.Hom.Basic import Mathlib.Algebra.Group.InjS...
Basic.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.Group.Commute.Units import Mathlib.Algebra.Group.Invertible.Defs import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Logic.Equiv.Defs /-! # Theorems...
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.Algebra.FreeAlgebra import Mathlib.SetTheory.Cardinal.Free /-! # Cardinality of free algebras This file contains some results about the cardinality of `FreeAlgebra`,...
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...
CompTypeclasses.lean
/- Copyright (c) 2021 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Ring.Equiv /-! # Propositional typeclasses on several ring homs This file contains three typeclasses used in the definitio...
Primitive.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Data.Nat.Prime.Basic import Mathlib.Data.Setoid.Partition.Card import Mathlib.GroupTheory.Gro...
Basic.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot, Eric Wieser -/ import Mathlib.Algebra.Notation.Pi.Defs import Mathlib.Logic.Function.Basic /-! # Very basic algebraic operations on pi types This file provi...
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...
Tauto.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, David Renshaw -/ import Mathlib.Tactic.CasesM import Mathlib.Tactic.Core import Mathlib.Lean.Elab.Tactic.Basic import Mathlib.Logic.Basic import Qq /-! The `tauto` tactic. -...
success_if_fail_with_msg.lean
import Mathlib.Tactic.SuccessIfFailWithMsg example : True := by success_if_fail_with_msg "No goals to be solved" trivial; trivial trivial example : Nat → Nat → True := by success_if_fail_with_msg "No goals to be solved" intro intro trivial trivial intros; trivial /-- info: Update with tactic e...
Equiv.lean
/- Copyright (c) 2024 Salvatore Mercuri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Salvatore Mercuri -/ import Mathlib.Topology.Algebra.Algebra /-! # Isomorphisms of topological algebras This file contains an API for `ContinuousAlgEquiv R A B`, the type of conti...
Function.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.Dynamics.Ergodic.Ergodic import Mathlib.MeasureTheory.Function.AEEqFun /-! # Functions invariant under (quasi)ergodic map In this file we prove tha...
CongrTheorems.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 Lean.Meta.Tactic.Cleanup import Lean.Meta.Tactic.Refl import Mathlib.Logic.IsEmpty /-! # Additions to `Lean.Meta.CongrTheorems` -/ namespace Lean.Meta initialize ...
path.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (******************************************************************************) (* ...
WithTop.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.Monoid.Unbundled.WithTop import Mathlib.Algebra.Order.Monoid.Canonical.Defs /-! # Adjoi...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...
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...
OfBasis.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.MeasureTheory.Measure.Haar.Basic import Mathlib.Analysis.InnerProductSpace.PiL2 /-! # Additive Haar measure constructed from a basis Given a ba...
Floor.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.Order /-! # Measurability of `⌊x⌋` etc In this file we prove that `Int.floor`, `Int.ceil`, `Int.fract`, `Nat...
UnsetOption.lean
import Mathlib.Tactic.UnsetOption set_option linter.style.setOption false set_option linter.unusedTactic false set_option pp.all true example : True := by run_tac let t : Option Bool := (← Lean.MonadOptions.getOptions).get? `pp.all -- should be true as set guard (t == true) trivial section unset_opt...
CharacterSpace.lean
/- Copyright (c) 2022 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Topology.Algebra.Module.WeakDual import Mathlib.Algebra.Algebra.Spectrum.Basic import Mathlib.Topology.ContinuousMap.Algebra import Mathlib.Data.Set....
DiracProba.lean
/- Copyright (c) 2024 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Topology.Separation.CompletelyRegular import Mathlib.MeasureTheory.Measure.ProbabilityMeasure /-! # Dirac deltas as probability measures and embedding of ...
Lattice.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Data.Set.Lattice.Image /-! # Unions and intersections of bounds Some results about upper and lower bounds over collections of sets. ## Imple...
ContinuedFractions.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Geißer, Michael Stoll -/ import Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries import Mathlib.Algebra.ContinuedFractions.Computation.Translations import...
Finset.lean
/- Copyright (c) 2021 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.Algebra.Group.Action.Pointwise.Finset import Mathlib.Algebra.GroupWithZero.InjSurj import Mathlib.Algebra.GroupWithZero.Action....
norm_num_ext.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Tactic.NormNum.BigOperators import Mathlib.Tactic.NormNum.GCD import Mathlib.Tactic.NormNum.IsCoprime import Mathlib.Tactic.NormNum.DivMod import Mathl...
SplitBy.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.Data.List.Chain /-! # Split a list into contiguous runs of elements which pairwise satisfy a relation. This file provides the...
Basic.lean
/- Copyright (c) 2023 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.AlgebraicTopology.SimplicialSet.KanComplex /-! # Quasicategories In this file we define quasicategories, a common model of infinity categories. We s...
Sheaf.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.Sheaf.Abelian import Mathlib.AlgebraicGeometry.Modules.Presheaf /-! # The category of sheaves of modules over a scheme In this file...
Basic.lean
/- Copyright (c) 2019 mathlib community. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Wojciech Nawrocki -/ import Mathlib.Data.Nat.Notation import Mathlib.Tactic.TypeStar import Mathlib.Util.CompileInductive /-! # Binary tree Provides binary tree st...
AbelLimit.lean
/- Copyright (c) 2024 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Tactic.Peel import Mathlib.Tactic.Positivity /-! # Abel's limit theorem I...
Introduction.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kyle Miller -/ /-! # Introduction to the conversion mode tactic Inside a tactic block, one can use the `conv` tactic to enter conversion mode. This mode allows one to...
Sublists.lean
/- Copyright (c) 2019 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Nat.Choose.Basic import Mathlib.Data.List.FinRange import Mathlib.Data.List.Perm.Basic import Mathlib.Data.List.Lex import Mathlib.Data.List.Induc...
Basic.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.HomCongr import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.Tactic.CategoryTheory.Elementwise /-! # Computation of `Over A` fo...
Opposite.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Action.Opposite import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Ring.Opposite /-! # Module operations on `Mᵐᵒᵖ` This file c...
ComonEquivalence.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.CoalgCat.Basic import Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric import Mathlib.CategoryTheory.Monoidal.Braided.Oppos...
Bifunctor.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Control.Functor import Mathlib.Tactic.Common /-! # Functors with two arguments This file defines bifunctors. A bifunctor is a function `F : Type* → Type* ...
slow_instances.lean
import Mathlib variable {K : Type*} [Field K] {x : K} -- This one is dismally slow: -- #time -- #synth NoZeroSMulDivisors ℕ K set_option maxHeartbeats 3000 in -- uses under 2000 as of 2025-08-06 /-- error: failed to synthesize Lean.Grind.NoNatZeroDivisors K Hint: Additional diagnostic information may be available...
Archimedean.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Order.Filter.AtTopBot.Group import Mathlib.Order.Filter.CountablyGenerated import Mathl...
Basic.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.Basic /-! # The upper half plane This file defines `UpperHalfP...
Monoidal.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Jack McKoen, Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic /-! # The monoidal category s...
Basic.lean
/- Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Interval.F...
Defs.lean
/- Copyright (c) 2024 Yudai Yamazaki. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yudai Yamazaki -/ import Mathlib.GroupTheory.GroupAction.ConjAct import Mathlib.GroupTheory.SemidirectProduct /-! # Group Extensions This file defines extensions of multiplicative a...
Diam.lean
/- Copyright (c) 2024 Rida Hamadani. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rida Hamadani -/ import Mathlib.Combinatorics.SimpleGraph.Metric /-! # Diameter of a simple graph This module defines the eccentricity of vertices, the diameter, and the radius of a s...
extraspecial.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 choice fintype bigop finset prime binomial. From mathc...
PartialOrder.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 Batteries.Tactic.Trans import Mathlib.Tactic.ExtendDoc import Mathlib.Tactic.Lemma import Mathlib.Tactic.SplitIfs import Mathlib.Tactic.TypeStar /-!...
Final.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.Filtered.Final /-! # Final functors between intervals -/ universe u instance Set.Ici.subtype_functor_final {J : Type u} [LinearOrder J] (j : J...
cyclotomic.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 div choice fintype tuple finfun bigop prime. From mat...
Connected.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Convex.Contractible import Mathlib.Analysis.Convex.Topology import Mathlib.Analysis.Normed.Module.Convex import Mathlib.LinearAlgebra.Di...
Discriminant.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.Algebra.Order.BigOperators.Group.LocallyFinite import Mathlib.RingTheory.Norm.Basic import Mathlib.RingTheory.Trace.Basic /-! # Discriminant of a fa...
Holder.lean
/- Copyright (c) 2025 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.MeasureTheory.Integral.Bochner.Basic /-! # Continuous bilinear maps on `MeasureTheory.Lp` spaces Given a continuous bilinear map `B : E →L[𝕜] F →L[𝕜]...
NormedSpace.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace import Mathlib.Geometry.Manifold.MFDeriv.FDeriv /-! ## Equivalence of manifold differe...
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, Floris van Doorn, Sébastien Gouëzel, Alex J. Best -/ import Mathlib.Algebra.Group.Defs /-! # Sums and products from lists This file provides basic definitions for `Li...
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, Devon Tuma -/ import Mathlib.Probability.ProbabilityMassFunction.Monad import Mathlib.Control.ULiftable /-! # Specific Constructions of Probability Mass Functions Thi...
Intersectivity.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.MeasureTheory.Integral.Average /-! # Bergelson's intersectivity lemma This file proves the Bergelson intersectivity lemma: In a finite measure space, a s...
Max.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Lattice.Fold /-! # Maximum and minimum of finite sets -/ assert_not_exists OrderedCommMonoid MonoidWithZe...
Star.lean
/- Copyright (c) 2023 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Data.NNReal.Defs import Mathlib.Data.Real.Star /-! # The non-negative real numbers are a `*`-ring, with the trivial `*`-structure -/ assert_not_exists ...
FinitePresentation.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.Data.Finite.Sum import Mathlib.RingTheory.FiniteType import Mathlib.RingTheory.Finiteness.Ideal import Mathlib.RingTheory.Ideal.Quotient.Operations imp...
Graph.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.Satisfiability import Mathlib.Combinatorics.SimpleGraph.Basic /-! # First-Order Structures in Graph Theory This file defines first-order ...
Hom.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yury Kudryashov, Amelia Livingston -/ import Mathlib.RingTheory.Coalgebra.Hom import Mathlib.RingTheory.Bialgebra.Basic /-! # Homomorphisms of `R`-bialgebras This file ...
Hom.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Hom.BoundedLattice /-! # Heyting algebra morphisms A Heyting homomorphism between two Heyting algebras is a bounded lattice homomorphism that prese...
SpectralNorm.lean
/- Copyright (c) 2025 María Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández -/ import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps import Mathlib.Analysis.Normed.Unbundled.InvariantExtension import Mathlib.A...
Adjunction.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Joël Riou -/ import Mathlib.CategoryTheory.Adjunction.Restrict import Mathlib.CategoryTheory.Adjunction.Whiskering import Mathlib.CategoryTheory.Sites.PreservesSheafification ...
Basic.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis -/ import Mathlib.Algebra.BigOperators.Field import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.InnerProductSpace.Defs /-! ...
DisjointCoproduct.lean
/- Copyright (c) 2021 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.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback /-! # Disjoint coproducts Defines disjoint c...
Prod.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.Algebra.Order.Sub.Defs import Mathlib.Algebra.Notation.Pi.Defs import Mathlib.Algebra.Notation.Prod /-! # Products of `OrderedSub` types. -/ assert_not_e...
LocalizationLocalization.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.RingTheory.Localization.AtPrime.Basic import Mathlib.RingTheory.Localization.Basic import Mathlib...
Convert.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Kyle Miller -/ import Mathlib.Tactic.CongrExclamation /-! # The `convert` tactic. -/ open Lean Meta Elab Tactic /-- Close the goal `g` using `Eq.mp v e`, where `v` is a ...
HasLocalization.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Predicate /-! Morphism properties equipped with a localized category If `C : Type u` is a category (with `[Category.{v} C]`), and `...
CardQuotient.lean
/- Copyright (c) 2025 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Alex J. Best, Xavier Roblot -/ import Mathlib.Data.Int.Associated import Mathlib.Data.Int.NatAbs import Mathlib.LinearAlgebra.Determinant import Mathlib.LinearAlgebra.FreeM...
IsFreeGroup.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn, Eric Wieser, Joachim Breitner -/ import Mathlib.GroupTheory.FreeGroup.Basic /-! # Free groups structures on arbitrary types This file defines the notion of free basis of a gr...
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....
Coeff.lean
/- Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Jalex Stark -/ import Mathlib.Algebra.Polynomial.Expand import Mathlib.Algebra.Polynomial.Laurent import Mathlib.Algebra.Polynomial.Eval.SMul import Mathli...
Maschke.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.TypeTags.Finite import Mathlib.Algebra.MonoidAlgebra.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace import Mathlib.RingTheory.SimpleMod...
Imo2001Q4.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.Intervals import Mathlib.Data.Int.Interval import Mathlib.GroupTheory.Perm.Fin /-! # IMO 2001 Q4 Let $n > 1$ be an odd integer and let $...
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.
Projective.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.Module.Projective import Mathlib.RingTheory.Finiteness.Cardinality /-! # Finite and projective modules -/ open Function (Surjective) namesp...
fingroup.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype div path...
PerfectClosure.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.CharP.Lemmas import Mathlib.FieldTheory.Perfect /-! # The perfect closure of a characteristic `p` ring ## Main definitions - `Perfec...