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RadonNikodym.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue /-! # Radon-Nikodym theorem Th...
Field.lean
/- Copyright (c) 2021 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.Field.Basic import Mathlib.Algebra.Order.Field.Canonical import Mathlib.Algebra.Order.Nonneg.Ring import Mathlib.Data.Nat.Cast.Order.Ring ...
Map.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 -/ import Mathlib.Dynamics.Ergodic.MeasurePreserving import Mathlib.MeasureTheory.Integral.Lebesgue.Add /-! # Behavior of the Lebesgue integral under ma...
Point.lean
/- Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula import Mathlib.LinearAlgebra.FreeModule.Norm import Mathlib.RingTheory.ClassGroup im...
AddRelatedDecl.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Floris van Doorn -/ import Mathlib.Init import Lean.Elab.DeclarationRange import Lean.Elab.Term /-! # `addRelatedDecl` -/ open Lean Meta Elab namespace Mathlib.Tactic ...
nmodule.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun monoid. (******************************************************************************) (* Additive group-like structures ...
GlobalAttributeIn.lean
/- Copyright (c) 2024 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang, Damiano Testa -/ import Lean.Elab.Command -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstring. import Ma...
borelize.lean
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic set_option autoImplicit true example [TopologicalSpace α] [inst : MeasurableSpace α] [BorelSpace α] : MeasurableSet (∅ : Set α) := by guard_target = @MeasurableSet α inst ∅ borelize α guard_target = @MeasurableSet α (borel α) ∅ apply MeasurableSe...
InvariantForm.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Lie.Semisimple.Defs import Mathlib.LinearAlgebra.BilinearForm.Orthogonal /-! # Lie algebras with non-degenerate invariant bilinear forms are s...
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, Yury Kudryashov -/ import Mathlib.Data.Set.SymmDiff import Mathlib.Order.SuccPred.Relation import Mathlib.Topology.Irreducible /-! # Connected subsets ...
Star.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Analysis.Calculus.FDeriv.Linear import Mathlib.Analysis.Calculus.FDeriv.Comp import Mathlib.Analysis.Calculus.FDeriv.Equiv import Mathlib.Analysis.CStarAlgeb...
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...
Get.lean
/- Copyright (c) 2019 mathlib community. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Wojciech Nawrocki -/ import Mathlib.Data.Num.Basic import Mathlib.Data.Ordering.Basic import Mathlib.Data.Tree.Basic /-! # Binary tree get operation In this file w...
LocalizationAway.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.RingTheory.Extension.Presentation.Basic /-! # Cotangent and localization away Let `R → S → T` be algebras such that `T` is the localization of `S...
Defs.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro, Yaël Dillies -/ import Mathlib.Data.Set.Operations import Mathlib.Logic.Function.Iterate import Mathlib.Order.Basic import Mathlib.Tactic.Coe import Mathl...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
Small.lean
/- Copyright (c) 2025 Antoine Chambert-Loir, María-Inés de Frutos-Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, Maria-Inés de Frutos-Fernandez -/ import Mathlib.LinearAlgebra.Finsupp.LinearCombination import Mathlib.RingTheory.FiniteT...
NoncommPiCoprod.lean
/- Copyright (c) 2022 Joachim Breitner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ import Mathlib.GroupTheory.OrderOfElement import Mathlib.Data.Nat.GCD.BigOperators import Mathlib.Order.SupIndep /-! # Canonical homomorphism from a finite famil...
Lattice.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Data.Fintype.Lattice import Mathlib.RingTheory.Finiteness.Basic /-! # Finite suprema of finite modules -/ namespace Submodule open Module variable...
FloorPow.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.Algebra.Order.Field.GeomSum import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Results on disc...
Trim.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.Measure.Typeclasses.SFinite /-! # Restriction of a measure to a sub-σ-algebra ## Main definitions * `MeasureTheory.Measure.trim`: restric...
Semiconj.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.Group.Semiconj.Defs import Mathlib.Algebra.Ring.Defs /-! # Semirings and ...
Minimal.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Peter Nelson -/ import Mathlib.Order.Antichain /-! # Minimality and Maximality This file proves basic facts about minimality and maximality of an element with respect to ...
Choose.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Floris van Doorn, Mario Carneiro, Reid Barton, Johan Commelin -/ import Mathlib.Util.Tactic import Mathlib.Logic.Function.Basic /-! # `choose` tactic Performs Skolemi...
Whiskering.lean
import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathlib.Algebra.Category.ModuleCat.Limits import Mathlib.Algebra.Category.ModuleCat.FilteredColimits import Mathlib.CategoryTheory.Sites.Equivalence universe u open CategoryTheory GrothendieckTopology section Small variable {C : Type u} [SmallCategory C] (J ...
Unitization.lean
/- Copyright (c) 2022 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.CStarAlgebra.Classes import Mathlib.Analysis.Normed.Algebra.Unitization /-! # The minimal unitization of a C⋆-algebra This file shows that when...
Sober.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.Topology.Sets.Closeds import Mathlib.Topology.Sets.OpenCover /-! # Sober spaces A quasi-sober space is a topological space where every irreducible closed s...
Ring.lean
/- Copyright (c) 2022 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer, Kevin Klinge, Andrew Yang -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Math...
Star.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.Order.Group.Abs import Mathlib.Algebra.Order.Monoid.Submonoid import Mathlib.Algebra.Order.Ring.Basic import Mathlib.Algebra.Order.Ring.Int import ...
WithLp.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Analysis.Normed.Lp.PiLp /-! # Derivatives on `WithLp` -/ section PiLp open Con...
Presheaf.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.FilteredColimitCommutesFiniteLimit import Mathlib.CategoryTheory.Limits.Elements /-! # Finite-limit-preserving presheaves In this...
Basic.lean
/- Copyright (c) 2024 Floris van Doorn and Hannah Scholz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Hannah Scholz -/ import Mathlib.Analysis.NormedSpace.Real import Mathlib.Data.ENat.Basic import Mathlib.Logic.Equiv.PartialEquiv import Mathlib.T...
Presheaf.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 import Mathlib.Algebra.Category.ModuleCat.Differentials.Basic /-! # The presheaf of differentials of a presheaf of modules ...
Cotangent.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.Algebra.Module.Torsion import Mathlib.Algebra.Ring.Idempotent import Mathlib.LinearAlgebra.Dimension.Finite import Mathlib.LinearAlgebra.Dimension.FreeAndStr...
NatAntidiagonal.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Order.Antidiag.Prod import Mathlib.Algebra.Order.Group.Nat import Mathlib.Data.Multiset.NatAntidiagonal /-! # Antidiagonals in ℕ × ℕ as finset...
Indicator.lean
/- Copyright (c) 2020 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Sébastien Gouëzel -/ import Mathlib.Analysis.SpecialFunctions.Pow.Continuity import Mathlib.MeasureTheory.Function.LpSpace.Basic import Mathlib.MeasureTheory.Measure.Real i...
Kernels.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.Algebra.Category.ModuleCat.EpiMono import Mathlib.CategoryTheory.ConcreteCategory.Elementwise /-! # The concrete (co)kernels in the category of modules ...
OfScalars.lean
/- Copyright (c) 2024 Edward Watine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Edward Watine -/ import Mathlib.Analysis.Analytic.ConvergenceRadius /-! # Scalar series This file contains API for analytic functions `∑ cᵢ • xⁱ` defined in terms of scalars `c₀, c₁, ...
HeytAlg.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Category.BddDistLat import Mathlib.Order.Heyting.Hom /-! # The category of Heyting algebras This file defines `HeytAlg`, the category of Heyting al...
VectorSpace.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Group.UniqueProds.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace /-! # A `ℚ`-vector space has `TwoUniqueSums`. -/ variable {G : Type*} /...
Dyadic.lean
/- Copyright (c) 2021 Apurva Nakade. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Apurva Nakade -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Order.Group.Basic import Mathlib.Algebra.Ring.Regular import Mathlib.GroupTheory.MonoidLocalization.Away impo...
IntermediateField.lean
/- Copyright (c) 2024 Jiedong Jiang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiedong Jiang -/ import Mathlib.FieldTheory.IntermediateField.Adjoin.Defs import Mathlib.Topology.Algebra.Field /-! # Continuous actions related to intermediate fields In this file we...
Interval.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.Data.Finset.Finsupp import Mathlib.Data.Finsupp.Order import Mathlib.Order.Interval.Finset.Basic /-! # Finite intervals of finitely supported functions T...
Localization.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.Ideal.MinimalPrime.Basic import Mathlib.RingTheory.Localization.AtPrime.Basic /-! # Minimal primes and localization We provide various results ...
RingDivision.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, Johan Commelin -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Div import Mathlib.RingTheory...
Basic.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Jujian Zhang, Yongle Hu -/ import Mathlib.Algebra.Colimit.TensorProduct import Mathlib.Algebra.DirectSum.Finsupp import Mathlib.Algebra.DirectSum.Module import Mathlib....
Classes.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.Analysis.Complex.Basic import Mathlib.Algebra.Star.NonUnitalSubalgebra /-! # Classes of C⋆-algebras This file defines classes for complex C⋆-algebras....
Basic.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.Defs import Mathlib.RingTheory.Ideal.Nonunits /-! # Local rings We prove basic properties of local rings. ...
DMatrix.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.Hom.Defs import Mathlib.Algebra.Group.Pi.Basic /-! # Dependent-typed matrices -/ universe u u' v w z /-- `DMatrix m n` is the type of dep...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
BaireMeasurable.lean
/- Copyright (c) 2024 Felix Weilacher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Felix Weilacher -/ import Mathlib.Topology.LocallyClosed import Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic ...
Real.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.MeasureTheory.Constructions.BorelSpace.Order import Mathlib.MeasureTheory.MeasurableSpace.Prod import Mathlib.MeasureTheory.Measure.Ty...
Pointwise.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Subgroup import Mathlib.Algebra.Ring.Subring.Basic import Mathlib.Algebra.Ring.Subsemiring.Pointwise /-! # Pointwise instances on `Sub...
Card.lean
/- Copyright (c) 2018 Mitchell Rowett. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Rowett, Kim Morrison -/ import Mathlib.GroupTheory.Coset.Basic import Mathlib.SetTheory.Cardinal.Finite /-! # Lagrange's theorem: the order of a subgroup divides the order o...
NormalForms.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.Tactic.Zify import Mathlib.Data.List.Sort import Mathlib.Tactic.Linarith import Mathlib.Tactic.NormNum.Ineq import Mathlib.Tactic.Ring.Basic /-! # Norma...
Range.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.Fintype.EquivFin import Mathlib.Data.ULift /-! # Finiteness of `Set.range` ## Implementation notes Each result in ...
Basic.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.Group.Torsion import Mathlib.Algebra.Notation.Pi.Basic import Mathlib.Data.FunLike.Basic import Mathlib.Logic.Function.Iterate import Mathlib.L...
Distinguished.lean
/- Copyright (c) 2024 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.RingTheory.Polynomial.Eisenstein.Basic import Mathlib.RingTheory.PowerSeries.Order /-! # Distinguished polynomial In this file we define the predicate `Po...
LocallySmall.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.Preserves.Ulift import Mathlib.CategoryTheory.Limits.IndYoneda import Mathlib.CategoryTheory.Limits.Indization.IndObject /-! # The...
Embedding.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.MeasureTheory.MeasurableSpace.Constructions import Mathlib.Tactic.FunProp /-! # Measurable embeddings and equivalences A measurable e...
DirectLimit.lean
/- Copyright (c) 2023 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.Algebra.Colimit.Module import Mathlib.LinearAlgebra.TensorProduct.Basic /-! # Tensor product and direct limits commute with each other. Given a family o...
Basic.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.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique import Mathlib.Topology.ContinuousMap.ContinuousSqrt import Mathlib.Topology.ContinuousMap.Sto...
finfun.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 tuple. ...
Basic.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.ContDiff.Operations import Mathlib.Analysis.Normed.Module.FiniteDimension /-! # Infinitely smooth "bump" func...
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...
CofilteredLimit.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.Topology.Category.Profinite.Basic import Mathlib.Topology.LocallyConstant.Basic import Mathlib.Topology.DiscreteQuotient import Mathlib.Topology.Category.TopCa...
Cofinal.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.GaloisConnection.Basic import Mathlib.Order.Interval.Set.Basic import Mathlib.Order.WellFounded /-! # Cofinal sets A se...
Sign.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Eric Wieser -/ import Mathlib.Data.Real.Basic import Mathlib.Tactic.NormNum.Inv /-! # Real sign function This file introduces and contains some results about `Real.sign` wh...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
Datatypes.lean
/- Copyright (c) 2024 Vasily Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasily Nesterov -/ import Mathlib.Init import Batteries.Data.Rat.Basic import Std.Data.HashMap.Basic /-! # Datatypes for the Simplex Algorithm implementation -/ namespace Mathlib.Ta...
finset.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 div seq. From mathcomp Require Import choice fintype finf...
RingHom.lean
/- Copyright (c) 2019 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston, Jireh Loreaux -/ import Mathlib.Algebra.Divisibility.Hom import Mathlib.Algebra.Ring.Hom.Defs import Mathlib.Data.Set.Insert /-! # Additional lemmas about homomo...
DeriveToExpr.lean
import Lean namespace DeriveToExprTests open Lean -- set_option trace.Elab.Deriving.toExpr true inductive MyMaybe (α : Type u) | none | some (x : α) deriving ToExpr run_cmd Elab.Command.liftTermElabM do guard <| "MyMaybe.some 2" == s!"{← Lean.PrettyPrinter.ppExpr <| toExpr (MyMaybe.some 2)}" run_cmd Elab.Com...
finfield.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 div tupl...
MvPolynomial.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.LinearAlgebra.DirectSum.Finsupp import Mathlib.Algebra.MvPolynomial.Eval import Mathlib.RingTheory.TensorProduct.Basic import Mathlib.Al...
Indization.lean
/- Copyright (c) 2025 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.FunctorCategory import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Types import Mathlib.CategoryTheory.Ab...
preorder.v
(* (c) Copyright 2006-2019 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 path fintype tup...
Basic.lean
/- Copyright (c) 2020 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp -/ import Mathlib.Algebra.Algebra.Spectrum.Basic import Mathlib.Algebra.Module.LinearMap.Basic import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathl...
Roth.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.Additive.AP.Three.Defs import Mathlib.Combinatorics.Additive.Corner.Defs import Mathlib.Combinatorics.SimpleGraph...
Reflection.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.Data.Fin.VecNotation import Mathlib.Algebra.BigOperators.Fin /-! # Lemmas for tuples `Fin m → α` This file contains alternative definitions of common opera...
AdjointAction.lean
/- Copyright (c) 2024 Frédéric Marbach. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Marbach -/ import Mathlib.Algebra.Lie.Abelian import Mathlib.Algebra.Lie.Derivation.Basic import Mathlib.Algebra.Lie.OfAssociative /-! # Adjoint action of a Lie algebra on ...
Productive.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.WSeq.Relation /-! # Productive weak sequences This file defines the property of a weak sequence being productive as never stalling – the ...
Connect.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.Algebra.Homology.Embedding.RestrictionHomology /-! # Connecting a chain complex and a cochain complex Given a chain complex `K`: `... ⟶ K.X 2 ⟶ K.X 1 ⟶ K.X 0`,...
Multivariate.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon -/ import Mathlib.Data.Fin.Fin2 import Mathlib.Data.TypeVec import Mathlib.Logic.Equiv.Defs /-! # Functors between the category of tuples of...
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...
LocalizerMorphism.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Equivalence /-! # Morphisms of localizers A morphism of localizers consists of a functor `F : C₁ ⥤ C₂` between two categories equip...
finset.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 div seq. From mathcomp Require Import choice fintype finf...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
Op.lean
/- Copyright (c) 2025 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer -/ import Mathlib.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Opposites /-! # The dualizing functor on `Cat` We define a (strict) functor `opFunctor`...
InjectiveSeminorm.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.Analysis.NormedSpace.PiTensorProduct.ProjectiveSeminorm import Mathlib.LinearAlgebra.Isomorphisms /-! # Injective seminorm on the tensor of a finite famil...
test_guard.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Inductive tree := Node { children : seq tree }. Inductive ptree (T : Type) := singleton of T | branch of list (ptree T). (* has *) Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :...
Exactness.lean
/- Copyright (c) 2024 Sihan Su. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sihan Su, Yongle Hu, Yi Song -/ import Mathlib.Algebra.Exact import Mathlib.RingTheory.LocalProperties.Submodule import Mathlib.RingTheory.Localization.Away.Basic import Mathlib.Algebra.Modu...
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. (********************************************************************...
Preorder.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton -/ import Mathlib.CategoryTheory.Equivalence import Mathlib.CategoryTheory.EqToHom import Mathlib.Order.Hom.Basic import Mathlib...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
Bifunctor.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Prod import Mathlib.CategoryTheory.Functor.Currying /-! # Lifting of bifunctors In this file, in the context of the localization of...
peel.lean
import Mathlib.Tactic.Peel import Mathlib.Topology.Instances.Real.Lemmas open Filter Topology /-! ## General usage -/ example (p q : Nat → Prop) (h₁ : ∀ x, p x) (h₂ : ∀ x, p x → q x) : ∀ y, q y := by peel 1 h₁ rename_i y guard_target =ₐ q y exact h₂ _ this example (p q : Nat → Prop) (h₁ : ∀ {x}, p x) (h₂ : ...
MulEquivHaarChar.lean
/- Copyright (c) 2025 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard -/ import Mathlib.MeasureTheory.Measure.Haar.Unique /-! # Scaling Haar measure by a continuous isomorphism If `G` is a locally compact topological group and `μ` is a reg...
Commute.lean
/- Copyright (c) 2014 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Algebra.GroupWithZero.Commute import Mathlib.Algebra.Ring.Commute /-! # Cast of natural numbers: lemmas about `Commute` -/ variable {α : Type*} nam...