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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 :...
Module.lean
/- Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Jujian Zhang -/ import Mathlib.Algebra.Colimit.DirectLimit import Mathlib.Algebra.DirectSum.Module import Mathlib.Data.Finset.Order import Mathlib.Gro...
Lattice.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Nicolò Cavalleri -/ import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Order.Group.Lattice import Mathlib.Topology.ContinuousMap.Algebra import Mathlib.Topology.Conti...
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...
WithDensity.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.MeasureTheory.Function.AEEqOfIntegral /-! # Vector measure defined by an integral Given a measure `μ` and...
Right.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.Monad.Adjunction import Mathlib.CategoryTheory.Monad.Equalizer /-! # Adjoint lifting This file gives two constructions for buildin...
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...
Cyclic.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.Group.TypeTags.Finite import Mathlib.Data.Nat.Totient import Mathlib.Data.ZMod.Aut import Mathlib.Data.ZMod.QuotientGroup import Mathlib.GroupT...
Ring.lean
/- Copyright (c) 2019 Kenny Lau, Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Jujian Zhang -/ import Mathlib.Algebra.Colimit.DirectLimit import Mathlib.Data.Finset.Order import Mathlib.RingTheory.FreeCommRing import Mathlib.Ring...
Nilpotent.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.Algebra.Lie.Solvable import Mathlib.Algebra.Lie.Quotient import Mathlib.Algebra.Lie.Normalizer import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib....
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
HurwitzZetaOdd.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.NumberTheory.LSeries.AbstractFuncEq import Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds import Mathlib.NumberTheory.LSeries.MellinEqDirichlet i...
Module.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.Algebra.Module.FinitePresentation import Mathlib.Algebra.Module.Torsion import Mathlib.LinearAlgebra.Dual.Lemmas import Mathlib.RingTheory.FiniteType import ...
Basic.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Topology.Algebra.Module.Stro...
SingularSet.lean
/- Copyright (c) 2023 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz -/ import Mathlib.AlgebraicTopology.SimplicialSet.Basic import Mathlib.AlgebraicTopology.TopologicalSimplex import Mathlib.CategoryTheory.Limit...
Monoidal.lean
/- Copyright (c) 2024 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.CategoryTheory.Subobject.Lattice import Mathlib.CategoryTheory.Monoidal.Braided.Basic import Mathlib.CategoryTheory.Dialectica.Basic /-! # The Dialect...
LocalIso.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.AlgebraicGeometry.Morphisms.LocalClosure /-! # Local isomorphisms A local isomorphism of schemes is a morphism that is source-locally an open imm...
Basic.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.Distributions.Gaussian.Real /-! # Gaussian distributions in Banach spaces We introduce a predicate `IsGaussian` for measures on a Banach spac...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
IsAlgClosed.lean
/- Copyright (c) 2023 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Nat.PrimeFin import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure import Mathlib.FieldTheory.IsAlgClosed.Classification import Mathlib.ModelTheory...
Polynomial.lean
/- Copyright (c) 2023 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.MvPolynomial.Eval import Mathlib.Analysis.Analytic.Constructions import Mathlib.Topology.Algebra.Module.Fini...
archimedean.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop or...
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...
Limits.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Topology.Sheaves.Sheaf import Mathlib.CategoryTheory.Sites.Limits import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic /-! # Presheaves in `C` have ...
Finsupp.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.BigOperators.Finsupp.Basic import Mathlib.Data.Finsupp.Indicator import Mathlib.Data.Fintype.BigOperators import Mathlib.Algebra.Group.Pointwise.Fi...
Conj.lean
/- Copyright (c) 2019 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Group.Units.Equiv import Mathlib.CategoryTheory.Endomorphism import Mathlib.CategoryTheory.HomCongr /-! # Conjugate morphisms by isomorphism...
IsOpenUnits.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.Jacobson.Ideal import Mathlib.Topology.Algebra.GroupWithZero import Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology /-! # Topological monoi...
Zero.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Closed.Cartesian import Mathlib.CategoryTheory.PUnit import Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects /-! # A cartesian closed categ...
Grading.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.DirectSum.Internal import Mathlib.Algebra.MonoidAlgebra.Basic import Mathlib.Algebra.MonoidAlgebra.Support import Mathlib.LinearAlgebra.Finsupp.SumPr...
Sups.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.Set.NAry import Mathlib.Order.SupClosed import Mathlib.Order.UpperLower.Closure /-! # Set family operations This file defines a few binary operation...
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, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland -/ import Mathlib.Algebra.Group.Defs import Mathlib.Algebra.GroupWithZero.Defs import Mathlib.Data.I...
LocalDiffeomorph.lean
/- Copyright (c) 2023 Michael Rothgang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Rothgang -/ import Mathlib.Geometry.Manifold.Diffeomorph import Mathlib.Topology.IsLocalHomeomorph /-! # Local diffeomorphisms between manifolds In this file, we define `C...
Lookup.lean
/- Copyright (c) 2024 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Mathlib.Lean.Meta.RefinedDiscrTree.Encode /-! # Matching with a RefinedDiscrTree This file defines the matching procedure for the `RefinedDiscrTree`. Th...
poly.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
Finsupp.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.BigOperators.Finsupp.Basic import Mathlib.Algebra.Module.End import Mathlib.GroupTheory.FreeAbelianGroup /-! # Isomorphism between `FreeAbelia...
perm.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 choice fintype tup...
bench_summary.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Lean.Elab.Command /-! # Summary of `!bench` results This file contains a script that converts data retrieved from the speed-center into a shorter, more access...
Restrict.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.Algebra import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital /-! # Restriction of the continuous functional calc...
Integral.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.MeasureTheory.Integral.Bochner.Basic import Mathlib.MeasureTheory.Group.Measure /-! # Bochner Integration on Groups We develop properties of inte...
EventuallyConst.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Floris van Doorn -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Order.Filter.AtTopBot.Basic import Mathlib.Order.Filter.Subsingleton /-! # Functions that...
Free.lean
/- Copyright (c) 2024 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Joel Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf import Mathlib.Algebra.Category.ModuleCat.Adjunctions /-! # The free presheaf of modules on a presheaf ...
Image.lean
/- Copyright (c) 2015 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Minchao Wu, Mario Carneiro -/ import Mathlib.Algebra.NeZero import Mathlib.Data.Finset.Attach import Mathlib.Data.Finset.Disjoint import Mathli...
DerivedSet.lean
/- Copyright (c) 2024 Daniel Weber. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Weber -/ import Mathlib.Topology.Perfect import Mathlib.Tactic.Peel /-! # Derived set This file defines the derived set of a set, the set of all `AccPt`s of its principal filter...
PontryaginDual.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Analysis.SpecialFunctions.Complex.Circle import Mathlib.Topology.Algebra.Group.CompactOpen /-! # Pontryagin dual This file defines the Pontryagin d...
Quotient.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Riccardo Brasca -/ import Mathlib.RingTheory.DedekindDomain.Dvr import Mathlib.RingTheory.IntegralClosure.IntegralRestrict import Mathlib.RingTheory.LocalRing.Quotient ...
NeLocus.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Junyan Xu -/ import Mathlib.Data.DFinsupp.Defs /-! # Locus of unequal values of finitely supported dependent functions Let `N : α → Type*` be a type family, assume that `N ...
Minpoly.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca, Johan Commelin -/ import Mathlib.Algebra.GCDMonoid.IntegrallyClosed import Mathlib.FieldTheory.Finite.Basic import Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed impo...
NerveAdjunction.lean
/- Copyright (c) 2024 Mario Carneiro and Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat import Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty i...
OneHypercover.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.Sites.Sheaf import Mathlib.CategoryTheory.Sites.ZeroHypercover /-! # 1-hypercovers Given a Grothendieck topology `J` on a category `C`, we defin...
Preadditive.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.CategoryTheory.Preadditive.AdditiveFunctor import Mathlib.CategoryTheory.Monoidal.Functor /-! # Preadditive monoidal categories A monoidal category is `M...
Subset.lean
/- Copyright (c) 2024 Miguel Marco. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miguel Marco -/ import Mathlib.Data.Set.Function import Mathlib.Data.Set.Functor /-! # Sets in subtypes This file is about sets in `Set A` when `A` is a set. It defines notation `↓∩` ...
StarAlgHom.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.Algebra.Algebra.Equiv import Mathlib.Algebra.Algebra.NonUnitalHom import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Algebra.Pi import Mathlib.Al...
Gauss.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.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes /-! # Gaussian Elimination algorithm The first step of `Linarith.SimplexAlgorithm.findPositiveVec...
Basic.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.Order.AddGroupWithTop import Mathlib.Algebra.Order.Monoid.Unbundled.MinMax import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Mathlib.A...
Subset.lean
/- Copyright (c) 2025 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine -/ import Mathlib.Dynamics.TopologicalEntropy.NetEntropy /-! # Topological entropy of subsets: monotonicity, closure, union This file contains general results about th...
Complex.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.Analysis.SpecialFunctions.Complex.Log import Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots /-! # Complex roots of unity In this file we show that th...
Mul.lean
/- Copyright (c) 2019 Jan-David Salchow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo -/ import Mathlib.Algebra.Algebra.Bilinear import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace /-! # Results about operator n...
GeneralizeProofs.lean
/- Copyright (c) 2022 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Kyle Miller -/ import Lean.Elab.Tactic.Config import Lean.Elab.Tactic.Location import Mathlib.Lean.Expr.Basic import Batteries.Lean.Expr /-! # The `generalize_proofs` tact...
Defs.lean
/- Copyright (c) 2019 Neil Strickland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Neil Strickland, Yury Kudryashov -/ import Mathlib.Algebra.Group.Semiconj.Defs /-! # Commuting pairs of elements in monoids We define the predicate `Commute a b := a * b = b * a` an...
quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype prim...
TaylorSeries.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.Analysis.Complex.CauchyIntegral /-! # Convergence of Taylor series of holomorphic functions We show that the Taylor series around some point `c : ℂ` of...
Trace.lean
/- Copyright (c) 2025 Iván Renison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Iván Renison -/ import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Analysis.InnerProductSpace.Spectrum import Mathlib.LinearAlgebra.Trace /-! # Traces in inner product spaces...
mxabelem.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...
EquivalenceAdditive.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.AlgebraicTopology.DoldKan.NCompGamma /-! The Dold-Kan equivalence for additive categories. This file defines `Preadditive.DoldKan.equivalence` which is the equ...
Init.lean
import Lean.Linter.Sets -- for the definition of linter sets import Mathlib.Tactic.Linter.CommandStart import Mathlib.Tactic.Linter.DeprecatedSyntaxLinter import Mathlib.Tactic.Linter.DirectoryDependency import Mathlib.Tactic.Linter.DocPrime import Mathlib.Tactic.Linter.DocString import Mathlib.Tactic.Linter.GlobalAttr...
InjSurj.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.GroupWithZero.Hom import Mathlib.Algebra.GroupWithZero.InjSurj import Mathlib.Algebra.Ring.Defs /-! # Pulling back rings ...
Lemmas.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.Order.Ring.Abs /-! # Further lemmas about the integers The distinction between this file and `Data.Int.Order.Basic` is not particularly clear. ...
Adjunction.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Sophie Morel -/ import Mathlib.CategoryTheory.Triangulated.Functor import Mathlib.CategoryTheory.Shift.Adjunction import Mathlib.CategoryTheory.Adjunction.Additive import Mathlib...
Fin.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Order.Interval.Finset.Fin import Mathlib.Data.Vector.Basic /-! # The structure of `Fintype (Fin n)` This file contains some basic results about the `Fintyp...
AdicTopology.lean
/- Copyright (c) 2021 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.RingTheory.Ideal.Maps import Mathlib.Topology.Algebra.Nonarchimedean.Bases import Mathlib.Topology.Algebra.UniformRing /-! # Adic topology Given a co...
FunctorCategory.lean
import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory deprecated_module (since := "2025-05-15")
WalkCounting.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Algebra.BigOperators.Ring.Nat import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected import Mathlib.Data.Finite.Card import Mathlib.Data.Set.Card im...
Lemmas.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Ken Lee, Chris Hughes -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Data.Fintype.Basic import Mathlib.Data.Int.GCD import Mathlib.RingTheory.Coprime.Basic /-...
Basic.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Data.Fintype.Basic import Mathlib.CategoryTheory.Discrete.Basic import Mathlib.CategoryTheory.Opposites import Mathlib.CategoryTheory.Category.ULift /-! #...
Accumulate.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.Data.Set.Lattice /-! # Accumulate The function `Accumulate` takes a set `s` and returns `⋃ y ≤ x, s y`. -/ variable {α β : Type*} {s : α → Set ...
Affine.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.Analysis.Convex.Side import Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine /-! # Oriented an...
UniformConvergence.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.Order.CompleteLattice.Group import Mathlib.Topology.ContinuousMap.Bounded.Basic import Mathlib.Topology.ContinuousMap.Compact import Mathlib.Topology.Met...
Bounds.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Eric Rodriguez -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Data.Nat.Cast.Order.Basic import Mathlib.Data.Nat.Choose.Basic /-...
Intervals.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Data.List.Lattice import Mathlib.Data.Bool.Basic import Mathlib.Order.Lattice /-! # Intervals in ℕ This file defines intervals of naturals. `List.Ico m n...
Goursat.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Graph import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.GroupTheory.QuotientGroup.Defs /-! # Goursat's lemma for subgroups This fi...
Pointwise.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.GroupTheory.GroupAction.SubMulAction import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # Pointwise monoid structures on SubMulAction This file provides ...
Gauge.lean
/- Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Analysis.Convex.Topology import Mathlib.Analysis.NormedSpace.Pointwise import Mathlib.Analysis.Seminorm import Mathlib.Analysis...
BirthdayProblem.lean
/- Copyright (c) 2021 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez -/ import Mathlib.Data.Fintype.CardEmbedding import Mathlib.Probability.UniformOn import Mathlib.Probability.Notation /-! # Birthday Problem This file proves Theorem 9...
MonoidHom.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.Algebra.Star.Basic /-! # Morphisms of star monoids This file defines the type of morphisms `StarMonoidHom` between monoids `A` and `B` where both `A` an...
Ideal.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.RingTheory.Ideal.BigOperators import Mathlib.RingTheory.Ideal.Span import Mathlib.Algebra.MonoidAlgebra.Defs /-! # Lemmas about ideals of `MonoidAlgebra` an...
Lebesgue.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.Measure.Decomposition.Hahn import Mathlib.MeasureTheory.Function.AEEqOfLIntegral import Mathlib.MeasureTheory.Measure.Sub /-! # Lebesgue decom...
Basic.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Algebra.Algebra.Opposite import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Algebra.Rat impor...
Pseudoelements.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.CategoryTheory.Abelian.Exact import Mathlib.CategoryTheory.Comma.Over.Basic import Mathlib.Algebra.Category.ModuleCat.EpiMono /-! # Pseudoelements in ab...
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...
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 ...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
ssrmatching.v
From Corelib Require Export ssrmatching.
MemoFix.lean
/- Copyright (c) 2022 Gabriel Ebner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gabriel Ebner, Edward Ayers -/ import Std.Data.HashMap.Basic import Mathlib.Init /-! # Fixpoint function with memoisation -/ universe u v open ShareCommon Std private unsafe abbrev ...
Domain.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.LinearAlgebra.Basis.VectorSpace import Mathlib.RingTheory.Flat.Localization /-! # Flat modules in domains We show that the tensor product of two injective ...
Constructions.lean
/- Copyright (c) 2022 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn -/ import Mathlib.Topology.FiberBundle.Basic /-! # Standard constructions on fiber bundles This file contains...
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, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.GroupTheory.MonoidLocalization.Away import Mathlib.Algebra.Algebra.Pi import Mathlib.RingTheory.I...
Basic.lean
/- Copyright (c) 2024 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.CategoryTheory.Subobject.Basic import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts /-! # Dialectica category We define the category `Dial` of ...
OfAlternating.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.LinearAlgebra.CliffordAlgebra.Fold import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic /-! # Extending an alternating map to the exterior algebra ## Main de...
tuple.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. From mathcomp Require Import seq choice fintype path. S...
LinearDisjoint.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.LinearAlgebra.TensorProduct.Tower import Mathlib.LinearAlgebra.TensorProduct.Finiteness import Mathlib.LinearAlgebra.TensorProduct.Submodule import Mathlib.LinearAlgeb...