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numdomain.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...
LinearPMap.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.LinearAlgebra.LinearPMap import Mathlib.Topology.Algebra.Module.Basic /-! # Partially defined linear operators over topological vector spaces We define bas...
Groupoid.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.CategoryTheory.Closed.Monoidal import Mathlib.CategoryTheory.Functor.Currying import Mathlib.CategoryTheory.Monoidal.FunctorCategory /-! # Functors ...
Set.lean
/- Copyright (c) 2022 Ian Benway. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ian Benway -/ import Mathlib.Tactic.Set import Mathlib.Tactic.Basic import Mathlib.Util.SleepHeartbeats import Qq example (x : Nat) (h : x = x) : x = x := by set! p := h set q : x = ...
ScottTopology.lean
/- Copyright (c) 2023 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Order.ScottContinuity import Mathlib.Topology.Order.UpperLowerSetTopology /-! # Scott topology This file introduces the Scott topology on a p...
Notation.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Eric Wieser -/ import Mathlib.Algebra.Group.Fin.Tuple import Mathlib.Data.Matrix.RowCol import Mathlib.Data.Fin.VecNotation import Mathlib.Tactic.FinCases import Mathlib.Alge...
ContinuousEval.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Topology.Hom.ContinuousEvalConst import Mathlib.Topology.ContinuousMap.Defs /-! # Bundled maps with evaluation continuous in both variables In this...
FiniteDimensional.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.Data.Matrix.Basic import Mathlib.LinearAlgebra.FiniteDimensional.Defs import Mathlib.LinearAlgebra.FreeModule...
Shrink.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.Group.Action.TransferInstance import Mathlib.Logic.Small.Defs import Mathlib.Tactic.SuppressCompilation /-! # Transfer group structures from `α` t...
GeomSum.lean
import Mathlib.Algebra.Group.NatPowAssoc import Mathlib.Algebra.Order.Field.GeomSum import Mathlib.Algebra.Order.Ring.GeomSum import Mathlib.Algebra.Ring.Regular import Mathlib.Tactic.Abel import Mathlib.Tactic.Positivity.Basic deprecated_module (since := "2025-06-19")
ApproximateUnit.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Topology.Algebra.Monoid /-! # Approximate units An *approximate unit* is a filter `l` such that multiplication on the left (or right) by `m : α` tends ...
Basic.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.InfinitePlace.Basic import Mathlib.RingTheory.LocalRing.RingHom.Basic import Mathlib.GroupTheory.Torsion /-! # Units of a numbe...
Subsingleton.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 Mathlib.Data.Set.Insert import Mathlib.Tactic.ByContra /-! # Subsingleton Defines the predicate `Subsingleton s : Prop`, saying that `s` has...
GCDMonoid.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson -/ import Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors /...
Density.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.Algebra.Order.Field.Rat import Mathlib.Data.Fintype.Card import Mathlib.Data.NNRat.Order import Mathlib.Data.Rat.Cast.CharZero import Mathlib.Tactic.Positi...
Cardinality.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.LinearAlgebra.Basis.Cardinality import Mathlib.LinearAlgebra.DFinsupp import Mathlib.LinearAlgebra.Isomorphisms import Mathlib.LinearAlgebra.StdBasis i...
Multiequalizer.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer /-! # Preservation of multicoequalizers Let `J : MultispanShape` and `d : MultispanIndex J C`. If `F : C ⥤ D`, we d...
SecondInter.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Geometry.Euclidean.Sphere.Basic /-! # Second intersection of a sphere and a line This file defines and proves basic results about the second intersection...
AsLimit.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.Topology.Category.LightProfinite.Basic /-! # Light profinite sets as limits of finite sets. We show that any light profinite set is isomorphic to ...
Isometry.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Data.Fintype.Lattice import Mathlib.Data.Fintype.Sum import Mathlib.Topology.Homeomorph.Lemmas import Mathlib.Topology.MetricSpace.Antilipschitz ...
binomial.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
Birthday.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.Algebra.Order.Group.OrderIso import Mathlib.SetTheory.Game.Ordinal import Mathlib.SetTheory.Ordinal.NaturalOps import Mathlib.T...
Quaternion.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Eric Wieser -/ import Mathlib.Algebra.Quaternion import Mathlib.Analysis.InnerProductSpace.Continuous import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.To...
Etale.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.AlgebraicGeometry.Morphisms.Etale import Mathlib.AlgebraicGeometry.PullbackCarrier import Mathlib.AlgebraicGeometry.Sites.BigZariski import Mathlib...
PushforwardContinuous.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf.Pushforward import Mathlib.Algebra.Category.ModuleCat.Sheaf import Mathlib.CategoryTheory.Sites.Over /-! # Pushforward of sh...
Grassmannian.lean
/- Copyright (c) 2025 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.RingTheory.Spectrum.Prime.FreeLocus /-! # Grassmannians ## Main definitions - `Module.Grassmannian`: `G(k, M; R)` is the `k`ᵗʰ Grassmannian of the `R`-module...
AlgebraicallyClosed.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity import Mathlib.NumberTheory.Cyclotomic.Basic /-! # Instances for HasEnoughRootsOfUnity We provide an instanc...
Compare.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.Data.Ordering.Basic import Mathlib.Order.Synonym /-! # Comparison This file provides basic results about orderings and comparison in linear orders. ...
Grade.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.Data.Set.Finite.Basic import Mathlib.Order.Atoms import Mathlib.Order.Grade import Mathlib.Order.Nat /-! # Finsets and multisets form a graded order This...
Init.lean
/- Copyright (c) 2023 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Init import Aesop /-! # Matroid Rule Set This module defines the `Matroid` Aesop rule set which is used by the `aesop_mat` tactic. Aesop rule sets only b...
Erased.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.Logic.Equiv.Defs /-! # A type for VM-erased data This file defines a type `Erased α` which is classically isomorphic to `α`, but erased in the VM. Th...
Epi.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.ConcreteCategory.EpiMono import Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective import Mathlib.CategoryTheory.Sites.EpiMono ...
Ulift.lean
/- Copyright (c) 2024 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.Algebra.Category.Grp.LargeColimits import Mathlib.Algebra.Category.Grp.Limits import Mathlib.Algebra.Module.CharacterModule import Mathlib.CategoryTheory.L...
vector.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 fi...
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, Manuel Candales -/ import Mathlib.Geometry.Euclidean.PerpBisector import Mathlib.Algebra.QuadraticDiscriminant /-! # Euclidean spaces This file makes some definitions and...
SeparatingDual.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.NormedSpace.HahnBanach.Extension import Mathlib.Analysis.NormedSpace.HahnBanach.Separation import Mathlib.Analysis.NormedSpace.Multiline...
ZeroLEOne.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.Order.Basic /-! # Typeclass expressing `0 ≤ 1`. -/ variable {α : Type*} open Function /-- Typeclas...
Relation.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Order.SuccPred.Archimedean /-! # Relations on types with a `SuccOrder` This file contains properties about relations on types with a `SuccOrder` ...
matrix.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 finfun f...
Limits.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.Topology.Category.CompHausLike.Limits import Mathlib.Topology.Category.LightProfinite.Basic /-! # Explicit limits and colimits This file applies ...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
Pi.lean
/- Copyright (c) 2023 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.MeasureTheory.Integral.Prod /-! # Integration with respect to a finite product of measures On a finite product of measure spaces, we show that a produc...
ssrnotations.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) (******************************************************************************) (* - Reserved notation for various arithmetic and algebraic operations: ...
IndObject.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.Limits.FinallySmall import Mathlib.CategoryTheory.Limits.Presheaf import Mathlib.CategoryTheory.Filtered.Small import Mathlib.CategoryTheo...
Basic.lean
/- Copyright (c) 2023 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.Dual.Lemmas /-! # Perfect pairings of modules A perfect pairing of two (left) modules may be defined either as: 1. A bilinear map `M × N → R`...
ZGroup.lean
/- Copyright (c) 2024 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.FieldTheory.Finite.Basic import Mathlib.GroupTheory.Abelianization.Finite import Mathlib.GroupTheory.Nilpotent import Mathlib.GroupTheory.SchurZassen...
OfNat.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.Init /-! # The `ofNat()` macro -/ /-- This macro is a shorthand for `OfNat.ofNat` combined with `no_index`. When writing lemmas about `OfNat.ofNat`, the t...
AbsConvex.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.LocallyConvex.BalancedCoreHull import Mathlib.Analysis.Convex.TotallyBounded /-! # Absolutely convex sets A set `s` in an commutative monoid `E` i...
maximal.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype finfun bigop finset prime binomial. Fro...
Colon.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Ring.Action.Pointwise.Set import Mathlib.LinearAlgebra.Quotient.Defs import Mathlib.RingTheory.Ideal.Maps /-! # The colon ideal This file defines `Subm...
Lemmas.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Yury Kudryashov -/ import Mathlib.Analysis.Asymptotics.Defs import Mathlib.Analysis.Normed.Group.Bounded import Mathlib.Analysis.Normed.Group.InfiniteSum import Mathlib.A...
SimplyConnected.lean
/- Copyright (c) 2022 Praneeth Kolichala. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Praneeth Kolichala -/ import Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps import Mathlib.Topology.Homotopy.Contractible import Mathlib.CategoryTheory.PUnit import Math...
gfunctor.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 fintype. From mathcomp Require Import bigop finset fingroup morphism automorphism. From math...
LocallyConstant.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Topology.LocallyConstant.Algebra import Mathlib.Topology.ContinuousMap.Basic import Mathlib.Topology.ContinuousMap.Algebra /-! # The algebra morphism from l...
Irrational.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Rat import Mathlib.Data.Nat.Prime.Int import Mathlib.Data.Rat.Sqrt imp...
RadonNikodym.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.Density import Mathlib.Probability.Kernel.WithDensity /-! # Radon-Nikodym derivative and Lebesgue decomposition for kern...
InjSurj.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, Floris van Doorn, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Algebra.Opposites import Mathlib.Algebra.GroupWit...
Multiset.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Algebra.GCDMonoid.Basic import Mathlib.Algebra.Order.Group.Multiset import Mathlib.Data.Multiset.FinsetOps import Mathlib.Data.Multiset.Fold /-! # GCD...
numdomain.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...
fingraph.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import seq path fintype. (******************************************...
LinearMap.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.Module.LinearMap.End import Mathlib.Algebra.Module.Submodule.Defs import Mathlib.Algebra.BigOperators.Group.Finset.Defs /-! # Linear maps in...
Interval.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.Group.Embedding import Mathlib.Algebra.Ring.CharZero import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Algebra.Order.Group.Unbundled.Int import M...
Quotient.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, David Kurniadi Angdinata, Devon Tuma, Riccardo Brasca -/ import Mathlib.Algebra.Polynomial.Div import Mathlib.Algebra.Polynomial.Eval.SMul import Mathlib.GroupTheory.GroupAction....
CorrectnessTerminating.lean
/- Copyright (c) 2020 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Computation.Translations import Mathlib.Algebra.ContinuedFractions.TerminatedStable import Mathlib.Algebra.ContinuedFrac...
Completion.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Robert Y. Lewis -/ import Mathlib.Algebra.Order.CauSeq.Basic import Mathlib.Algebra.Ring.Action.Rat import Mathlib.Tactic.FastInstance /-! # Cauchy completion This fi...
Impartial.lean
/- Copyright (c) 2020 Fox Thomson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fox Thomson -/ import Mathlib.SetTheory.Game.Basic import Mathlib.Tactic.NthRewrite import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "This module is now at `Combinatoria...
Addition.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, Miyahara Kō -/ import Mathlib.Data.Option.Defs import Mathlib.Tactic.CC.MkProof /-! # Process when an new equation is added to a congruence closure -/ unive...
Basic.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.Data.Countable.Defs import Mathlib.Data.Fin.Tuple.Basic import Mathlib.Data.ENat.Defs import Mathlib.Logic.Equiv.Nat /-! # Countable types In this ...
ProdAssoc.lean
import Mathlib.Tactic.ProdAssoc variable {α β γ δ : Type*} example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ := by exact (prod_assoc% : (α × β) × (γ × δ) ≃ α × (β × γ) × δ) example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ := prod_assoc% example : (α × β) × (γ × δ) ≃ α × (β × γ) × δ := (prod_assoc% : _ ≃ α × β × γ × δ)...
Hahn.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.VectorMeasure.Basic import Mathlib.Order.SymmDiff /-! # Hahn decomposition This file proves the Hahn decomposition theorem (signed version). ...
QExpansion.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.Complex.TaylorSeries import Mathlib.Analysis.Complex.UpperHalfPlane.Exp import Mathlib.NumberTheory.ModularForms.Basic import Mathlib.NumberTh...
Invariants.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.RepresentationTheory.Basic import Mathlib.RepresentationTheory.FDRep /-! # Subspace of invariants a group representation This file introduces the s...
LSum.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Mathlib.Algebra.Module.Equiv.Basic import Mathlib.Algebra.Module.Submodule.LinearMap import Mathlib.Li...
FunctorToTypes.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.Category.Preorder import Mathlib.CategoryTheory.Types import Mathlib.Data.Set.Basic /-! # The functor from `Set X` to types Given `X : Type u`, ...
Continuous.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic import Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving import Mathlib.Topology.Alg...
Defs.lean
/- Copyright (c) 2014 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn -/ import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra.Field.Defs /-! # Linear ordered (semi)fields A ...
integral_char.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...
positivity.lean
import Mathlib.Tactic.Positivity import Mathlib.Data.Complex.Trigonometric import Mathlib.Data.Real.Sqrt import Mathlib.Data.ENNReal.Basic import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Analysis.SpecialFunctions.Pow.Real import Mathlib.Analysis.SpecialFunctions.Log.Basic import Mathlib.Analysis.SpecialFuncti...
Powerset.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, Kyle Miller -/ import Mathlib.Data.Finset.Powerset import Mathlib.Data.Set.Finite.Basic /-! # Finiteness of the powerset of a finite set ## Implementa...
Limit.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.Order.SetIsMax import Mathlib.Order.SuccPred.Limit /-! # Limit elements in Set.Ici If `J` is a linearly ordered type, `j : J`, and `m : Set.Ici j` is successor...
SupIndep.lean
/- Copyright (c) 2021 Aaron Anderson, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Kevin Buzzard, Yaël Dillies, Eric Wieser -/ import Mathlib.Data.Finset.Lattice.Union import Mathlib.Data.Finset.Pairwise import Mathlib.Data.Finset.Prod i...
SeparableDegree.lean
/- Copyright (c) 2021 Jakob Scholbach. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Scholbach -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.FieldTheory.Separable /-! # Separable degree This file contains basics about the separable degree of a polynom...
Satisfiability.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.ModelTheory.Ultraproducts import Mathlib.ModelTheory.Bundled import Mathlib.ModelTheory.Skolem import Mathlib.Order.Filter.AtTopBot.Basic /-! # First-...
Basic.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Richard Hill, Andrew Yang -/ import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathlib.Algebra.Category.ModuleCat.Limits import Mathlib.Topology.Algebra.Module.ModuleTopology impo...
WithWeakNamespace.lean
/- Copyright (c) 2021 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Daniel Selsam, Gabriel Ebner -/ import Mathlib.Init /-! # Defines `with_weak_namespace` command. Changes the current namespace without causing scoped things t...
Basic.lean
/- Copyright (c) 2024 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.RingTheory.Invariant.Defs import Mathlib.RingTheory.IntegralClosure.IntegralRestrict /-! # Invariant Extensions of Rings Given an extension of ring...
Equiv.lean
import Mathlib.Data.Int.Order.Units import Mathlib.GroupTheory.Perm.Finite example : orderOf (-1 : ℤˣ) = 2 := orderOf_eq_prime (Int.units_sq _) (by decide)
CompletelyRegular.lean
/- Copyright (c) 2023 Matias Heikkilä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Matias Heikkilä -/ import Mathlib.Topology.UrysohnsLemma import Mathlib.Topology.UnitInterval import Mathlib.Topology.Compactification.StoneCech import Mathlib.Topology.Order.Lattice ...
HomologicalBicomplex.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Joël Riou -/ import Mathlib.Algebra.Homology.HomologicalComplex /-! # Bicomplexes Given a category `C` with zero morphisms and two complex shapes `c₁ : ComplexShape I₁` a...
Counting.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.Combinatorics.SimpleGraph.Clique import Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform import Mathlib.Data.Real.Basic imp...
Bilipschitz.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Topology.MetricSpace.Antilipschitz import Mathlib.Topology.MetricSpace.Lipschitz /-! # Bilipschitz equivalence A common pattern in Mathlib is to replac...
fraction.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 ssrAC choice tuple ...
PolarCoord.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.Function.Jacobian import Mathlib.MeasureTheory.Measure.Lebesgue.Complex import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deri...
Index.lean
/- Copyright (c) 2021 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Finset import Mathlib.Algebra.GroupWithZero.Subgroup import Mathlib.Data.Finite.Card import Mathlib.Data.Finite.Pr...
interval_inference.v
(* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice. From mathcomp Require Import order ssralg ssrnum ssrint interval. (**md********************************************************...
OpenMapping.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.Topology.Baire.Lemmas import Mathlib.Topology.Algebra.Group.Pointwise /-! # Open mapping theorem for morphisms of topological groups We prove t...
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, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.Algebra.BigOperators.Group.Finset.Defs import Mathlib.Algebra.Regular.Basic import Mathlib.Data.F...
Semiring.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kevin Kappelmann -/ import Mathlib.Algebra.Order.Floor.Defs import Mathlib.Algebra.Order.Field.Basic import Mathlib.Tactic.Linarith /-! # Lemmas on `Nat.floor` and `Na...
choice.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (**************************************************...
LapMatrix.lean
/- Copyright (c) 2023 Adrian Wüthrich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adrian Wüthrich -/ import Mathlib.Combinatorics.SimpleGraph.AdjMatrix import Mathlib.LinearAlgebra.Matrix.PosDef /-! # Laplacian Matrix This module defines the Laplacian matrix of a...