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Group.lean
/- Copyright (c) 2020. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Massot -/ import Mathlib.Tactic.Ring import Mathlib.Tactic.FailIfNoProgress import Mathlib.Algebra.Group.Commutator /-! # `group` tactic Normalizes expressions in the langu...
Quot.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Simon Hudon -/ import Mathlib.Data.QPF.Multivariate.Basic /-! # The quotient of QPF is itself a QPF The quotients are here defined using a surjective function and its r...
EpsilonNFA.lean
/- Copyright (c) 2021 Fox Thomson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fox Thomson, Yaël Dillies, Anthony DeRossi -/ import Mathlib.Computability.NFA import Mathlib.Data.List.ReduceOption /-! # Epsilon Nondeterministic Finite Automata This file contains th...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
AsymptoticEquivalent.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.Asymptotics.Theta /-! # Asymptotic equivalence In this file, we define the relation `IsEquivalent l u v`, which means that `u-v` is litt...
End.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Bicategory.Basic import Mathlib.CategoryTheory.Monoidal.Category /-! # Endomorphisms of an object in a bicategory, as a monoidal category. ...
AdjoinRoot.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.AdjoinRoot import Mathlib.RingTheory.Localization.Away.Basic /-! The `R`-`AlgEquiv` b...
Basic.lean
import Mathlib.Tactic.CategoryTheory.Bicategory.Basic open CategoryTheory Mathlib.Tactic BicategoryLike open Bicategory universe w v u variable {B : Type u} [Bicategory.{w, v} B] variable {a b c d : B} example {f j : a ⟶ d} {g : a ⟶ b} {h : b ⟶ c} {i : c ⟶ d} (η : f ⟶ g ≫ (h ≫ i)) (θ : (g ≫ h) ≫ i ⟶ j) : η ...
Complex.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Kexing Ying, Eric Wieser -/ import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv import Mathlib.Analysis.SpecialFunctions.Pow.Complex /-! # Quadratic forms over the comp...
Closure.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Order.Interval.Set.OrdConnected import Mathlib.Order.Minimal import Mathlib.Order.UpperLower.Principal /-! # Upper and lower clo...
Colimits.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.Ring.Basic import Mathlib.CategoryTheory.Limits.HasLimits /-! # The category of commutative rings has all colimits. This file uses a "pr...
GaussEisensteinLemmas.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Nat.Prime.Factorial import Mathlib.NumberTheory.LegendreSymbol.Basic /-! # Lemmas of Gauss and Eisenstein This file contains the Lemmas of Gauss and...
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....
NoetherianObject.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.Subobject.Lattice import Mathlib.CategoryTheory.ObjectProperty.ContainsZero import Mathlib.CategoryTheory.ObjectProperty.EpiMono import Mathlib.Ca...
Augment.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.Single /-! # Augmentation and truncation of `ℕ`-indexed (co)chain complexes. -/ noncomputable section open CategoryTheory Limits Homol...
FiniteDimensional.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.FieldTheory.Minpoly.Field import Mathlib.Algebra.Polynomial.Module.AEval import Mathlib.Algebra.Module.Torsion /-! # Polynomial modules in finite dimensions...
linarith.lean
import Mathlib.Tactic.Linarith import Mathlib.Tactic.Linarith.Oracle.FourierMotzkin import Mathlib.Algebra.BigOperators.Group.Finset.Pi import Mathlib.Algebra.Order.Ring.Rat import Mathlib.Order.Interval.Finset.Nat private axiom test_sorry : ∀ {α}, α set_option linter.unusedVariables false set_option autoImplicit fals...
ConeCategory.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.Adjunction.Comma import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal import Mathlib....
archimedean.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 bigop or...
SmallAffineZariski.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.AlgebraicGeometry.AffineScheme import Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology /-! # The small affine Zariski site `X.AffineZariskiSite` ...
orderedzmod.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
Abs.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.Group.Even import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Order.Group.Lattice /...
Weierstrass.lean
/- Copyright (c) 2021 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, David Kurniadi Angdinata -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Algebra.CubicDiscriminant import Mathlib.RingTheory.Nilpotent.Defs import Mathlib.Tactic.Fiel...
Path.lean
/- Copyright (c) 2024 Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialSet.Horn /-! # Paths in simplicial sets A path in a simplicial set `X` of length `n` is a directed p...
Primrec.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.Algebra.Order.Ring.Nat import Mathlib.Logic.Encodable.Pi import Mathlib.Logic.Function.Iterate /-! # The primitive recursive functions The primitive ...
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 ...
LocallyConvex.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.ContinuousMap.Algebra import Mathlib.Topology.Algebra.Module.LocallyConvex /-! # The space of continuous maps is a locally convex space In...
FundamentalDomain.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Alex Kontorovich, Heather Macbeth -/ import Mathlib.MeasureTheory.Group.Action import Mathlib.MeasureTheory.Group.Pointwise import Mathlib.MeasureTheory.Integral.Lebe...
Lemmas.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Order.Nonneg.Field import Mathlib.Data.Rat.Cast.Defs import Mathlib.Tactic.Positivity.Basic /-! # Some exiled lemmas about cas...
Multiplication.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Scott Carnahan -/ import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.GroupWithZero.Regular import Mathlib.Algebra.Module.BigOperators import Mathl...
Sigma.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.Faithful import Mathlib.Data.Sigma.Basic /-! # Sigma instances for additive and multiplicative actions This file defines instances f...
Lift.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, Kim Morrison -/ import Mathlib.Algebra.MonoidAlgebra.Defs /-! # Lifting monoid algebras This file defines `liftNC`. For the definition of `MonoidAlge...
MidpointZero.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.LinearAlgebra.AffineSpace.Midpoint /-! # Midpoint of a segment for characteristic zero We collect lemmas th...
Inhabit.lean
import Mathlib.Tactic.Inhabit namespace InhabitTests universe u -- Most basic test (prop) noncomputable example {p : Prop} [Nonempty p] : Inhabited p := by inhabit p assumption -- Most basic test (nonprop) noncomputable example {α : Type} [Nonempty α] : Inhabited α := by inhabit α assumption -- Confirms in...
Real.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.Group.Pointwise.Interval import Mathlib.Topology.MetricSpace.Pseu...
Randomisation.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.Analysis.Fourier.FiniteAbelian.Orthogonality import Mathlib.Combinatorics.Additive.Dissociation /-! # Randomising by a function of dissociated support Th...
Elementwise.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Tactic.CategoryTheory.Elementwise import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Limits.Shapes.Kernels import Mathlib.CategoryT...
DominatedConvergence.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Patrick Massot -/ import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic import Mathlib.MeasureTheory.Measure.Real import Mathlib.Order.Filter.Indi...
JoyalTrick.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.ModelCategory.CategoryWithCofibrations import Mathlib.CategoryTheory.MorphismProperty.Limits /-! # A trick by Joyal In order to construct a m...
Basic.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler, Stefan Kebekus -/ import Mathlib.Analysis.Analytic.IsolatedZeros /-! # Meromorphic functions Main statements: * `MeromorphicAt`: definition of meromorphy at a point ...
CardIntervalMod.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.Data.Int.Interval import Mathlib.Data.Int.ModEq import Mathlib.Data.Nat.Count import Mathlib.Data.Rat.Floor import Mathlib.Order.Interval.Finset.Nat /-! # Cou...
Basic.lean
/- Copyright (c) 2024 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Mathlib.Init /-! # Basic Definitions for `RefinedDiscrTree` We define * `Key`, the discrimination tree key * `LazyEntry`, the partial, lazy computation o...
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...
BoundedCompactlySupported.lean
/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ import Mathlib.Topology.ContinuousMap.Bounded.Normed /-! # Compactly supported bounded continuous functions The two-sided ideal of compactly supported bounded continuou...
EssSup.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.Constructions.BorelSpace.Order import Mathlib.MeasureTheory.Measure.Count import Mathlib.Order.Filter.ENNReal import Mathlib.Probability.Unif...
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...
Idempotent.lean
/- Copyright (c) 2022 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Group.Idempotent import Mathlib.Algebra.GroupWithZero.Defs /-! # Idempotent elements of a group with zero -/ assert_not_exists Ring ...
Measurable.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.Basic import Mathlib.Analysis.Calculus.Deriv.Slope import Mathlib.Analysis.Normed.Operator.BoundedLinear...
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
ring_quotient.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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
Basic.lean
/- Copyright (c) 2018 Kevin Buzzard, Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Patrick Massot -/ -- This file is to a certain extent based on `quotient_module.lean` by Johannes Hölzl. import Mathlib.Algebra.Group.Subgroup.Pointwise ...
BoundedVariation.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.Order.Interval.Set.ProjIcc import Mathlib.Tactic.Finiteness import Mathlib.Topology.Semicontinuous import Mathlib.Topology.UniformSpace.UniformCo...
TextBased.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Batteries.Data.String.Matcher import Mathlib.Data.Nat.Notation import Lake.Util.Casing -- Don't warn about the lake import: the above file has almost no ...
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 ...
FactorizedRational.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.Meromorphic.Divisor import Mathlib.Analysis.Meromorphic.IsolatedZeros import Mathlib.Analysis.Meromorphic.NormalForm import Mathlib.Analysis.M...
Basic.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Analysis.Convex.StrictConvexBetween import Mathlib.Analysis.InnerProductSpace.Convex import Mathlib.Analysis.Normed.Affine.Convex import Mathlib.Geometry.E...
Basic.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.Category import Mathlib.CategoryTheory.Functor.Trifunctor /-! # Actions from a monoidal category on a category Given a monoida...
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.Group.AddChar import Mathlib.MeasureTheory.MeasurableSpace.Defs /-! # Measurable space instance for additive characters This file endows `AddChar...
ConjExponents.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.Data.ENNReal.Holder /-! # Real conjugate exponents This file defines Hölder triple and Hölder conjugate exponents in `ℝ` and `...
seq.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat. (******************************************************...
Submodule.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, Alexander Bentkamp -/ import Mathlib.Algebra.Algebra.Basic import Mathlib.LinearAlgebra.Basis.Basic /-! # Bases of submodules -/ open Function Set Sub...
Pointwise.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.Submonoid.Pointwise import Mathlib.Algebra....
rsuffices.lean
import Mathlib.Tactic.RSuffices import Mathlib.Tactic.ExistsI import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Set.Defs set_option autoImplicit true /-- These next few are duplicated from `rcases/obtain` tests, with the goal order swapped. -/ example : True := by rsuffices ⟨n : ℕ, h : n = n, -⟩ : ∃ n : ℕ, n = n ...
ZNum.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Order.Ring.Cast import Mathlib.Data.Int.Cast.Lemmas import Mathlib.Data.Num.Lemmas /-! # Properties of the `ZNum` representation of int...
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.RingTheory.LocalRing.Basic /-! # Maximal ideal of local rings We define the maximal ideal of a local ring as the ideal of all no...
PartialEquiv.lean
/- Copyright (c) 2024 Gabin Kolly. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Gabin Kolly, David Wärn -/ import Mathlib.ModelTheory.DirectLimit import Mathlib.Order.Ideal /-! # Partial Isomorphisms This file defines partial isomorphisms between fir...
Image.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 -/ import Batteries.Tactic.Congr import Mathlib.Data.Option.Basic import Mathlib.Data.Prod.Basic import Mathlib.Data.Set.Subsingleton import Mathlib.Dat...
Deriv.lean
/- Copyright (c) 2022 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.MellinTransform import Mathlib.Analysis.SpecialFunctions.Gamma.Basic /-! # Derivative of the Gamma function This file shows that the (comple...
Cardinality.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.Ring.GeomSum import Mathlib.Data.Finite.Sum import Mathlib.Data.Fintype.Units import Mathlib.GroupTheory.Grou...
IsValuedIn.lean
/- Copyright (c) 2025 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan, Oliver Nash -/ import Mathlib.Algebra.Module.Submodule.Invariant import Mathlib.LinearAlgebra.RootSystem.Defs /-! # Root pairings taking values in a subring This file...
Basic.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, Bhavik Mehta, Jakob von Raumer -/ import Mathlib.CategoryTheory.Limits.HasLimits /-! # Preservation and reflection of (co)limits. There are various distinct ...
Push.lean
/- Copyright (c) 2019 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Simon Hudon, Alice Laroche, Frédéric Dupuis, Jireh Loreaux -/ import Lean.Elab.Tactic.Location import Mathlib.Data.Set.Defs import Mathlib.Logic.Basic import Mathlib.O...
Equiv.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.AsymptoticEquivalent import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calcul...
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, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne -/ import Mathlib.Data.Set.Subsingleton import Mathlib.Order.BooleanAlgebra.Set import Mathlib.Order.Inter...
Functoriality.lean
/- Copyright (c) 2025 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic import Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree /-! # Functoria...
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, Bryan Gin-ge Chen -/ import Mathlib.Order.Heyting.Basic /-! # (Generalized) Boolean algebras This file sets up the theory of (generalized) Boolean algebras. A Boolea...
Lemmas.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro -/ import Mathlib.Data.Finset.Insert import Mathlib.Data.Finset.Lattice.Basic /-! # Lemmas about the lattice struct...
LinearCombination'.lean
/- Copyright (c) 2022 Abby J. Goldberg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Abby J. Goldberg, Mario Carneiro -/ import Mathlib.Tactic.Ring /-! # linear_combination' Tactic In this file, the `linear_combination'` tactic is created. This tactic, which works...
TCSynth.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison -/ import Mathlib /-! # Test against slow typeclass synthesis This file tests against regression in typeclass synthesis speed. The tests below became fas...
OrderDual.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl -/ import Mathlib.Algebra.Order.Group.Synonym import Mathlib.Algebra.Order.Monoid.Unbundled.Defs /-! # Unbundled ordere...
Bernstein.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.BigOperators.Field import Mathlib.Analysis.Convex.Gauge import Mathlib.Analysis.Normed.Order.Lattice import Mathlib.RingTheory.Polynomial.Bernstein...
Lattice.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Kim Morrison -/ import Mathlib.CategoryTheory.Functor.Currying import Mathlib.CategoryTheory.Subobject.FactorThru import Mathlib.CategoryTheory.Subobject.WellPowered import...
Basic.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Adam Topaz -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.CategoryTheory.Limits.Preserves.Basic import Mathlib.CategoryTheory.Limits.Types.Colimits ...
Int.lean
/- Copyright (c) 2024 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Data.ZMod.QuotientGroup import Mathlib.GroupTheory.Index import Mathlib.LinearAlgebra.FreeModule.PID /-! # Inde...
IsSupported.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.Embedding.Basic import Mathlib.Algebra.Homology.Opposite import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex /-! # Support of homol...
Continuum.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.SetTheory.Cardinal.Arithmetic /-! # Cardinality of continuum In this file we define `Cardinal.continuum` (notation: `𝔠`, localized in `Cardinal`) ...
Limits.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Dagur Asgeirsson, Filippo A. E. Nuccio, Riccardo Brasca -/ import Mathlib.CategoryTheory.Extensive import Mathlib.CategoryTheory.Limits.Preserves.Finite import Mathlib.To...
Main.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.Requests def help : String := "Mathlib4 caching CLI Usage: cache [COMMAND] Commands: # No privilege required get [ARGS] Download l...
Uniform.lean
/- Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Combinatorics.SimpleGraph.Density import Mathlib.Data.Nat.Cast.Order.Field impo...
BigOperators.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.Submonoid.Basic import Mathlib.Algebra.Grou...
Orientation.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Data.Complex.Module import Mathlib.LinearAlgebra.Orientation /-! # The standard orientation on `ℂ`. This had previously been in `LinearAlgebra.Orie...
BinaryEntropy.lean
/- Copyright (c) 2023 Adomas Baliuka. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adomas Baliuka -/ import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog import Mathlib.Analysis.Convex.SpecificFunctions.Basic /-! # Properties of Shannon q-ary entropy and binary en...
countalg.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 bigop ss...
Nat.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.Nat.Bits import Mathlib.Data.Nat.Pairing /-! # Equivalences involving `ℕ` This file defines some additional constructive equivalences using `Enc...
classfun.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
LinearOrderWithPosMulPosEqZero.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Damiano Testa, Kevin Buzzard -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Algebra.Order.GroupWithZero.Canonical /-! An example of a `LinearOrderedCommMon...
LocallyCompact.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, Yury Kudryashov -/ import Mathlib.Topology.Compactness.Compact /-! # Locally compact spaces This file contains basic results about locally compact spac...
Map2.lean
/- Copyright (c) 2014 Parikshit Khanna. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro -/ import Mathlib.Data.List.Defs import Mathlib.Tactic.Common /-! # Map₂ Lemmas This file conta...
EpiMono.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.Limits.Shapes.Pullback.CommSq /-! # Relation between mono/epi and pullback/pushout squares In this file, monomorphisms and epimorphisms are char...
Bilinear.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Basic import Mathlib.Analysis.Normed.Operator.LinearIsometry import Mathlib.Analysi...