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Piecewise.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.ContinuousOn /-! ### Continuity of piecewise defined functions -/ open Set Filter Function Topology Filter variable {α β : Type*} [Topologi...
LocalRing.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.LocalRing.Module import Mathlib.RingTheory.LocalRing.ResidueField.Ideal import Mathlib.RingTheory.Unramified.Field import Mathlib.RingTheory.Unram...
MeanValue.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.Deriv.AffineMap import Mathlib.Analysis.Calculus.Deriv.Comp import Mathlib.Analysis.Calculus.Deriv.Mul import Ma...
Parity.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.Algebra.Ring.Parity import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Algebra.Group.Int.Even /-! # Basic parity lemmas for the ring `ℤ` See note [fou...
Pi.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Logic.Encodable.Pi import Mathlib.MeasureTheory.Group.Measure import Mathlib.MeasureTheory.MeasurableSpace....
Basic.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang, Yury Kudryashov -/ import Mathlib.Data.Fintype.Option import Mathlib.Topology.Homeomorph.Lemmas import Mathlib.Topology.Sets.Opens /-! # The OnePoint Compactification We ...
Biproducts.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.Algebra.Group.Pi.Lemmas import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts import Mathlib.Algebra.Category.ModuleCat.Abelian import Mathlib.Algeb...
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...
NormalForm.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 /-! # Normal form of meromorphic functions and continuous extension If a function `f` is meromorphic on `U` and if `g` d...
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.Monoid.Unbundled.TypeTags import Mathlib.Algebra.Order.Monoid.Canonical.Defs /-! # Bund...
Basic.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Yaël Dillies -/ import Mathlib.Algebra.Group.Units.Basic import Mathlib.Algebra.GroupWithZero.NeZero import Mathlib.Algebra.Order.Group...
Tight.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Josha Dekker -/ import Mathlib.MeasureTheory.Measure.RegularityCompacts import Mathlib.Topology.Order.Lattice /-! # Tight sets of measures A set of measures is tight if f...
Opposite.lean
/- Copyright (c) 2022 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.RingTheory.Congruence.Basic import Mathlib.GroupTheory.Congruence.Opposite /-! # Congruences on the opposite ring This file defines the order isomorphism ...
Order.lean
/- Copyright (c) 2025 Vasilii Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasilii Nesterov -/ import Mathlib.Tactic.Order.CollectFacts import Mathlib.Tactic.Order.Preprocessing import Mathlib.Tactic.Order.Graph.Basic import Mathlib.Tactic.Order.Graph.Tarja...
MapLemmas.lean
/- Copyright (c) 2023 Alex Keizer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex Keizer -/ import Mathlib.Data.Vector.Basic import Mathlib.Data.Vector.Snoc /-! This file establishes a set of normalization lemmas for `map`/`mapAccumr` operations on vectors -/ ...
Lemmas.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.Group.TypeTags.Hom import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Algebra.Ring.Parity /-! # Cast of integers (additional theorems) This ...
Primal.lean
/- Copyright (c) 2024 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Algebra.GroupWithZero.Divisibility /-! # Submonoid of primal elements -/ assert_not_exists RelIso Ring /-- The sub...
OrdConnectedComponent.lean
/- Copyright (c) 2022 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.OrdConnected import Mathlib.Data.Set.Lattice.Image /-! # Order connected components of a set In this file we define `Set.ordConn...
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...
BddOrd.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.CategoryTheory.Category.Bipointed import Mathlib.Order.Category.PartOrd import Mathlib.Order.Hom.Bounded /-! # The category of bounded orders This define...
MGFAnalytic.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.Probability.Moments.ComplexMGF import Mathlib.Analysis.SpecialFunctions.Complex.Analytic import Mathlib.Analysis.Calculus.Taylor /-! # The moment generati...
LieBracket.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.VectorField import Mathlib.Geometry.Manifold.ContMDiffMFDeriv import Mathlib.Geometry.Manifold.MFDeriv.NormedSpace import Mathl...
HomComplexShift.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomotopyCategory.HomComplex import Mathlib.Algebra.Homology.HomotopyCategory.Shift import Mathlib.Algebra.Module.Equiv.Basic /-! Shifting cocha...
Frontend.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yury Kudryashov, Floris van Doorn, Jon Eugster -/ import Mathlib.Data.Nat.Notation import Mathlib.Data.String.Defs import Mathlib.Data.Array.Defs import Mathlib.Lean.Ex...
ContextFreeGrammar.lean
/- Copyright (c) 2023 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak -/ import Mathlib.Computability.Language /-! # Context-Free Grammars This file contains the definition of a context-free grammar, which is a grammar that has a single no...
abelian.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 choice div fintype finfun bigop finset prime. From ma...
Integrable.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Function.L1Space.Integrable import Mathlib.Probability.Independence.Basic /-! # Independence of functions implies that the measure...
Unramified.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.Unramified.Locus import Mathlib.RingTheory.LocalProperties.Basic /-! # The meta properties of unramified ring homomorphisms. -/ namespace Ring...
Basic.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Utensil Song -/ import Mathlib.Algebra.RingQuot import Mathlib.LinearAlgebra.TensorAlgebra.Basic import Mathlib.LinearAlgebra.QuadraticForm.Isometry import Mathlib.LinearAlge...
Opposite.lean
/- Copyright (c) 2024 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Monoidal.Opposite /-! # If `C` is braided, so is `Cᵒᵖ`. Todo: we should also do `Cᵐᵒᵖ...
Basic.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Tactic.FinCases import Mathlib.Topology.Connected.LocallyConnected import Mathlib.Topology.Sets.Closeds /-! ...
Polynomial.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.Topology.Algebra.Polynomial import Mathlib.Topology.ContinuousMap.Star import Mathlib.Topology.UnitInterval import Mathlib.Algebra.Star.Subalgebra /-! # C...
closed_field.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 seq. From mathcomp Require Import fintype generic_...
Dickson.lean
/- Copyright (c) 2021 Julian Kuelshammer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Julian Kuelshammer -/ import Mathlib.Algebra.CharP.Algebra import Mathlib.Algebra.CharP.Invertible import Mathlib.Algebra.CharP.Lemmas import Mathlib.Algebra.EuclideanDomain.Field ...
Imo1964Q1.lean
/- Copyright (c) 2020 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard -/ import Mathlib.Tactic.IntervalCases import Mathlib.Data.Nat.ModEq import Mathlib.Tactic.Ring /-! # IMO 1964 Q1 (a) Find all positive integers $n$ for which $2^n-1$ is...
NaturalOps.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.Ordinal.Family import Mathlib.Tactic.Abel import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "This mo...
Explode.lean
import Mathlib.Tactic.Explode import Mathlib.Data.Real.Basic set_option linter.unusedVariables false open Lean /-- info: true_iff : ∀ (p : Prop), (True ↔ p) = p 0 │ │ p ├ Prop 1 │ │ x✝ │ ┌ True ↔ p 2 │ │ trivial │ │ True 3 │1,2 │ Iff.mp │ │ p 4 │1,3 │ ∀I │ (True ↔ p) → p 5 │ │...
Basis.lean
/- Copyright (c) 2020 Jalex Stark. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jalex Stark, Kim Morrison, Eric Wieser, Oliver Nash, Wen Yang -/ import Mathlib.Data.Matrix.Basic /-! # Matrices with a single non-zero element. This file provides `Matrix.single`. The ...
Lattice.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, Kim Morrison -/ import Mathlib.Data.List.Basic /-! # Lattice structure of lists This files pro...
UniformMulAction.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Module.Opposite import Mathlib.Topology.UniformSpace.Completion import Mathlib.Topology.Algebra.IsUniformGroup.Defs /-! # Multiplicative act...
Union.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.Lattice.Fold import Mathlib.Data.Finset.Union /-! # Relating `Finset.biUnion` with lattice operations This file shows `Finset.biUnion` co...
OpenImmersion.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.AlgebraicGeometry.Morphisms.UnderlyingMap /-! # Open immersions A morphism is an open immersion if the underlying map of spaces is an open embedding `f : ...
SubboxInduction.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.Box.SubboxInduction import Mathlib.Analysis.BoxIntegral.Partition.Tagged /-! # Induction on subboxes In this file we prove (se...
SuccAboveOrderIso.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.Order.Fin.Basic import Mathlib.Data.Fintype.Basic import Mathlib.Tactic.FinCases /-! # The order isomorphism `Fin (n + 1) ≃o {i}ᶜ` Given `i : Fin (n + 2)`, we...
Lemmas.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton -/ import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Topology.Connected.LocallyConnected import Mathlib.Top...
Classifier.lean
/- Copyright (c) 2024 Charlie Conneen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Charlie Conneen, Pablo Donato, Klaus Gy -/ import Mathlib.CategoryTheory.Limits.Shapes.RegularMono import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq import Mathlib.CategoryT...
Basic.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Junyan Xu, Yury Kudryashov -/ import Mathlib.Analysis.Complex.Liouville import Mathlib.Analysis.Calculus.Deriv.Polynomial import Mathlib.Data.Complex.FiniteDimensional impo...
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...
Algebraic.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.FieldTheory.IntermediateField.Basic import Mathlib.FieldTheory.Minpoly.Basic import Mathlib.FieldTheory.Tower import Mathlib.LinearAlgebra.FreeModule.StrongR...
vcharacter.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype...
YoungDiagram.lean
/- Copyright (c) 2022 Jake Levinson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jake Levinson -/ import Mathlib.Data.Finset.Preimage import Mathlib.Data.Finset.Prod import Mathlib.Data.SetLike.Basic import Mathlib.Order.UpperLower.Basic /-! # Young diagrams A You...
Imo2001Q2.lean
/- Copyright (c) 2021 Tian Chen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tian Chen -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # IMO 2001 Q2 Let $a$, $b$, $c$ be positive reals. Prove that $$ \frac{a}{\sqrt{a^2 + 8bc}} + \frac{b}{\sqrt{b^2 + 8ca}}...
Sym.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.Finset.Sym import Mathlib.Data.Sym.Sym2.Order import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Lemmas on `Finset.sum` and `Finset.prod` inv...
Lookmap.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 Batteries.Logic import Batteries.Data.List.Basic import Mathlib.Tactic.TypeStar /-! ##...
PathComponentOne.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.Topology.Algebra.OpenSubgroup import Mathlib.Topology.Connected.LocPathConnected /-! # The path component of the identity in a locally path connected to...
Interval.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.Order.Interval.Set.OrdConnected import Mathlib.Order.Filter.SmallSets import Mathlib.Order.Filter.AtTopBot.Basic import Mathlib.Order.Filter.Bases.Fi...
Covering.lean
/- Copyright (c) 2022 Antoine Labelle, Rémi Bottinelli. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle, Rémi Bottinelli -/ import Mathlib.Combinatorics.Quiver.Cast import Mathlib.Combinatorics.Quiver.Symmetric import Mathlib.Data.Sigma.Basic import Math...
Statement.lean
/- Copyright (c) 2023 Lean FRO LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ /-! # If normalization Rustan Leino, Stephan Merz, and Natarajan Shankar have recently been discussing challenge problems to compare proof assistants. (See https://lean...
Lemmas.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker -/ import Mathlib.Algebra.Polynomial.Eval.Degree import Mathlib.Algebra.Prime.Lemmas /-! # Theory of degrees of polynomials S...
ssralg.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 div seq. From mathcomp Require Import choice fintype finf...
Solid.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Functor.KanExtension.Pointwise import Mathlib.Condensed.Functors import Mathlib.Condensed.Limits /-! # Solid modules This file co...
StronglyMeasurable.lean
/- Copyright (c) 2025 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.MeasureTheory.Constructions.Polish.Basic import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic /-! # Results about strongly measurable functi...
Deriv.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne -/ import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.LogDeriv import Mathlib.Analysis.SpecialFuncti...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
Bounds.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.Algebra.Order.GroupWithZero.Unbundled.Basic import Mathlib.Order.Bounds.Basic import Mathlib.Order.Bounds.Image /-! #...
Polynomial.lean
/- Copyright (c) 2025 Jingting Wang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jingting Wang -/ import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.RingTheory.KrullDimension.PID import Mathlib.RingTheory.LocalRing.ResidueField.Fiber /-! # Krull dimensi...
Finite.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison -/ import Mathlib.Algebra.Module.Torsion import Mathlib.LinearAlgebra.Dimension.Finite /-! # Results relating rank and tors...
Ordnode.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Order.Compare import Mathlib.Data.List.Defs import Mathlib.Data.Nat.PSub import Mathlib.Data.Option.Basic /-! # Ordered sets This file defines a data...
TFAE.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.RingTheory.DedekindDomain.Basic import Mathlib.RingTheory.DiscreteValuationRing.Basic import Mathlib.RingTheory.Finiteness.Ideal import Mathlib.RingTheory.Id...
Kernels.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.Limits.Shapes.Kernels import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero /-! # Preserving (co)kernels Constructions to relate the ...
BigOperators.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.BigOperators.WithTop import Mathlib.Data.NNReal.Basic import Mathlib.Data.ENNReal.Inv /-! # Properties of big operators exten...
Opposite.lean
/- Copyright (c) 2024 Daniel Carranza. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Carranza -/ import Mathlib.CategoryTheory.Enriched.Ordinary.Basic import Mathlib.CategoryTheory.Monoidal.Braided.Basic /-! # The opposite category of an enriched category Wh...
Maps.lean
/- Copyright (c) 2021 Hunter Monroe. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hunter Monroe, Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Dart import Mathlib.Data.FunLike.Fintype import Mathlib.Logic.Embedding.Set /-! # Maps between graphs This file ...
rat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import prime fintype fi...
Period.lean
/- Copyright (c) 2024 Emilie Burgun. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Emilie Burgun -/ import Mathlib.Dynamics.PeriodicPts.Lemmas import Mathlib.GroupTheory.Exponent import Mathlib.GroupTheory.GroupAction.Basic /-! # Period of a group action This modul...
CondexpL2.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.InnerProductSpace.Projection.Basic import Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique import Mathlib.MeasureTheory.Function.L2Spa...
tfae.lean
import Mathlib.Tactic.TFAE import Mathlib.Tactic.SuccessIfFailWithMsg open List set_option autoImplicit true section zeroOne example : TFAE [] := by tfae_finish example : TFAE [P] := by tfae_finish end zeroOne namespace two axiom P : Prop axiom Q : Prop axiom pq : P → Q axiom qp : Q → P example : TFAE [P, Q] :=...
Algebra.lean
/- Copyright (c) 2025 Christian Merten, Yi Song, Sihan Su. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Yi Song, Sihan Su -/ import Mathlib.RingTheory.Flat.FaithfullyFlat.Basic import Mathlib.RingTheory.Ideal.Over import Mathlib.RingTheory.LocalRing...
RamificationGroup.lean
/- Copyright (c) 2022 Michail Karatarakis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michail Karatarakis -/ import Mathlib.RingTheory.LocalRing.ResidueField.Basic import Mathlib.RingTheory.Valuation.ValuationSubring /-! # Ramification groups The decomposition su...
Sphere.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.Analysis.Calculus.Deriv.Inv import Mathlib.Analysis.Complex.Circle import Mathlib.Analysis.NormedSpace.BallAction import Mathlib.Analysis.SpecialFunc...
GaloisObjects.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.CategoryTheory.Galois.Basic import Mathlib.CategoryTheory.Limits.FintypeCat import Mathlib.CategoryTheory.Limits.Preserves.Limits import Mathlib.Ca...
FunctorExtension.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Idempotents.Karoubi /-! # Extension of functors to the idempotent completion In this file, we construct an extension `functorExtension₁` of func...
eqtype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool. (********************************************************************...
HomologicalComplex.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.Additive import Mathlib.Algebra.Homology.ShortComplex.Exact import Mathlib.Algebra.Homology.ShortComplex.Preadditive import Mathlib.Tactic.Linar...
Imo2013Q5.lean
/- Copyright (c) 2021 David Renshaw. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Renshaw -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Ring.GeomSum import Mathlib.Algebra.Ring.Regular import Mathlib.Data.Real.Archimedean impo...
test_order_conv.v
From mathcomp Require Import all_boot all_order. Import Order.Theory. Section dual_of_dual. Context (disp : Order.disp_t). Let eq_dual_dual_preorderType (T : preorderType disp) : Order.Preorder.on T = Order.Preorder.on T^d^d := erefl. Let eq_dual_dual_porderType (T : porderType disp) : Order.POrder.on T = Order....
HarrisKleitman.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.Order.Ring.Canonical import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Combinatorics.SetFamily.Compression.Down import Mathlib.Data.Fintype.Powe...
Localization.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.Localization.Bousfield import Mathlib.CategoryTheory.Sites.Sheafification /-! # The sheaf category as a localized category In this file, it is s...
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...
mxpoly.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 choice seq. From mathcomp Require Import div fintype tupl...
RingEquiv.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Ring.Opposite import Mathlib.Algebra.BigOperators.Group.Finset.Defs /-! # Re...
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.Constructions.EpiMono import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic /-! # Monomorphisms and epimorphisms in functor categorie...
Semiconj.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.GroupWithZero.Units.Basic import Mathlib.Algebra.Group.Semiconj.Units /-! # Lemmas about semiconjugate elements in a `GroupWithZero`. -/ ass...
InferParam.lean
import Mathlib.Tactic.InferParam namespace InferParamTest theorem zero_le_add (a : Nat) (ha : 0 ≤ a := Nat.zero_le a) : 0 ≤ a + a := calc 0 ≤ a := ha _ ≤ a + a := Nat.le_add_left _ _ theorem zero_le_add' (a : Nat) (ha : 0 ≤ a := by decide) : 0 ≤ a + a := zero_le_add a ha example : 0 ≤ 2 + 2 := by fail_if_succ...
Copy.lean
/- Copyright (c) 2023 Yaël Dillies, Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Mitchell Horner -/ import Mathlib.Algebra.Order.Group.Nat import Mathlib.Combinatorics.SimpleGraph.Subgraph /-! # Containment of graphs This file introdu...
Grothendieck.lean
/- Copyright (c) 2020 Bhavik Mehta, Edward Ayers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Edward Ayers -/ import Mathlib.CategoryTheory.Sites.Sieves import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer import Mathlib.CategoryTheory.Category.P...
BoolIndicator.lean
/- Copyright (c) 2022 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson, Leonardo de Moura -/ import Mathlib.Order.BooleanAlgebra.Set /-! # Indicator function valued in bool See also `Set.indicator` and `Set.piecewise`. -/ assert_not_...
div.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (******************************************************************************) (* Th...
Grade.lean
/- Copyright (c) 2022 Yaël Dillies, Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Vladimir Ivanov -/ import Mathlib.Data.Int.SuccPred import Mathlib.Order.Fin.Basic /-! # Graded ord...
Sensitivity.lean
/- Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Michael Han, Chris Hughes, Robert Y. Lewis, Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Johan Commelin, Jesse Michael Han, Chris Hughes, Robert Y. Lewis, Patrick Massot -/ import...