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Ineq.lean
/- Copyright (c) 2022 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Tactic.NormNum.Eq import Mathlib.Algebra.Order.Field.Defs import Mathlib.Algebra.Order.Invertible import Mathlib.Algebra.Order.Monoid.WithTop import Ma...
Ring.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.GradedMonoid import Mathlib.Algebra.DirectSum.Basic import Mathlib.Algebra.Ring.Associator /-! # Additively-graded multiplicative structures on `⨁ i...
prime.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 path. From mathcomp Require Import choice fintype div bigop. (*************************...
Factors.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, Mario Carneiro -/ import Mathlib.Algebra.BigOperators.Ring.List import Mathlib.Data.Nat.GCD.Basic import Mathlib.Data.Nat.Prime.Basic import Ma...
character.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 choice ssrnat seq. From mathcomp Require Import path div fintype...
Functor.lean
/- Copyright (c) 2016 Leonardo de Moura. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.Control.Basic import Mathlib.Data.Set.Defs import Mathlib.Data.Set.Lattice.Image import Mathlib.Data.Set.Notation /-! # Functoriality of `Set` ...
ssreflect.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Export ssreflect. Global Set SsrOldRewriteGoalsOrder. Global Set Asymmetric Patterns. Global Set Bullet Behavior "None". #[deprecated(sinc...
ssrmatching.v
From Corelib Require Export ssrmatching.
KAbstractPositions.lean
/- Copyright (c) 2023 Jovan Gerbscheid. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jovan Gerbscheid -/ import Mathlib.Init import Lean.HeadIndex import Lean.Meta.ExprLens import Lean.Meta.Check /-! # Find the positions of a pattern in an expression This file def...
IntegralRestrict.lean
/- Copyright (c) 2023 Andrew Yang, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.DedekindDomain.IntegralClosure import Mathlib.RingTheory.RingHom.Finite import Mathlib.RingTheory.Localization.LocalizationLocalizat...
Basic.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Hom.Basic import Mathlib.Logic.Equiv.Basic import Mathlib.Tactic....
Defs.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Fabian Glöckle, Kyle Miller -/ import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Mathlib.LinearAlgebra.BilinearMap import Mathlib.LinearAlgebra.Span.Defs /-!...
Projective.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, David Swinarski -/ import Mathlib.Algebra.Module.FinitePresentation import Mathlib.Algebra.Module.Projective import Mathlib.LinearAlgebra.Dimension.Constructions import Mathl...
PNatToNat.lean
/- Copyright (c) 2025 Vasilii Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasilii Nesterov -/ import Mathlib.Data.PNat.Basic /-! # `pnat_to_nat` This file implements the `pnat_to_nat` tactic that shifts `PNat`s in the context to `Nat`. ## Implementation...
BifunctorHomotopy.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.Bifunctor import Mathlib.Algebra.Homology.Homotopy /-! # The action of a bifunctor on homological complexes factors through homotopies Given a...
TensorProduct.lean
/- Copyright (c) 2025 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Yunzhou Xie -/ import Mathlib.Algebra.Central.Basic import Mathlib.RingTheory.Flat.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace /-! # Lemmas about tensor product...
LocallyUniformConvergence.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.UniformSpace.UniformConvergence /-! # Locally uniform convergence We define a sequence of functions `Fₙ` to *converge locally uniforml...
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...
Opposite.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.Group.Commute.Defs import Mathlib.Algebra.Group.InjSurj import Mathlib.Algebra.Opposites import Mathlib.Tactic.Spread /-! # Group structures on the mult...
Associated.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, Anne Baanen -/ import Mathlib.Algebra.BigOperators.Finsupp.Basic import Mathlib.Algebra.Group.Submonoid.Membership import Mathlib.Algebra.GroupWithZero....
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.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Group.Submonoid.Membership import Mathlib.Algebra.Order.BigOperators.Group.List import Mathli...
Degree.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.Subsemigroup.Operations import Mathlib.Algebra.MonoidAlgebra.Support import Mathlib.Order.Filter.Extr /-! # Lemmas about the `sup` and `in...
Enrichment.lean
/- Copyright (c) 2024 Daniel Carranza. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniel Carranza, Joël Riou -/ import Mathlib.CategoryTheory.Enriched.Ordinary.Basic import Mathlib.CategoryTheory.Closed.Monoidal /-! # A closed monoidal category is enriched in itse...
mxalgebra.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 b...
Basic.lean
/- Copyright (c) 2020 Ashvni Narayanan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ashvni Narayanan -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Group.Subgroup.Basic import Mathlib.Algebra.Ring.Subring.Defs import Mathlib.Algebra.Ring.Subsemiring.Bas...
Multiset.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.List.Chain import Mathlib.Data.Multiset.Sort import Mathlib.Logic.Equiv.List /-! # `Encodable` and `Denumerable` instances for `Multiset` -/ var...
Multiset.lean
/- Copyright (c) 2021 Ruben Van de Velde. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ruben Van de Velde, Daniel Weber -/ import Mathlib.Algebra.BigOperators.Group.Multiset.Defs import Mathlib.Algebra.Order.BigOperators.GroupWithZero.List /-! # Big operators on a m...
ModuleTopology.lean
/- Copyright (c) 2024 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Will Sawin -/ import Mathlib.Topology.Algebra.Module.Equiv import Mathlib.RingTheory.Finiteness.Cardinality import Mathlib.Algebra.Algebra.Bilinear /-! # A "module topol...
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.LinearAlgebra.Countable import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.MeasureTheory.Group.FundamentalDomain import Mathlib.MeasureTheory.Mea...
Shrink.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.SuccPred.Basic import Mathlib.Logic.Small.Defs /-! # Order instances on Shrink If `α : Type v` is `u`-small, we transport various order related instances...
Recurse.lean
/- Copyright (c) 2022 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Heather Macbeth -/ import Mathlib.Util.AtomM /-! # Running `AtomM` metaprograms recursively Tactics such as `ring` and `abel` are implemented using the `AtomM` monad,...
Frobenius.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Algebra.ZMod import Mathlib.Data.Nat.Multiplicity import Mathlib.FieldTheory.Perfect import Mathlib.RingTheory.WittVector.Basic import Mathlib....
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. ...
all_field.v
From mathcomp Require Export algC. From mathcomp Require Export algebraics_fundamentals. From mathcomp Require Export algnum. From mathcomp Require Export closed_field. From mathcomp Require Export cyclotomic. From mathcomp Require Export falgebra. From mathcomp Require Export fieldext. From mathcomp Require Export fin...
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, Floris van Doorn -/ import Mathlib.Geometry.Manifold.ContMDiff.Defs /-! ## Basic properties of `C^n` functions between manifolds In this file, we show that stan...
Orthogonality.lean
/- Copyright (c) 2023 Yaël Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Bhavik Mehta -/ import Mathlib.Algebra.BigOperators.Expect import Mathlib.Algebra.Group.AddChar import Mathlib.Analysis.RCLike.Inner /-! # Orthogonality of c...
Compact.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot -/ import Mathlib.Topology.Algebra.Group.Pointwise import Mathlib.Topology.Sets.Compacts /-! # Additional results on topological groups ...
Grp_.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.Algebra.Category.Grp.Limits import Mathlib.CategoryTheory.Monoidal.Grp_ /-! # Yoneda embedding of `Grp_ C` We show that group objects are exactly those who...
Defs.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri, Yury Kudryashov -/ import Mathlib.Tactic.Continuity import Mathlib.Tactic.Lift import Mathlib.Topology.Defs.Basic /-! # Continuous bundled maps In this file we de...
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...
Basic.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.RingTheory.Norm.Defs import Mathlib.FieldTheory.PrimitiveElement import Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly import Mathlib.LinearAlgebra.Matrix.ToL...
Extreme.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Convex.Extreme import Mathlib.Dynamics.Ergodic.Function import Mathlib.Dynamics.Ergodic.RadonNikodym import Mathlib.Probability.ConditionalP...
NonUnitalSubsemiring.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Algebra.Group.Subsemigroup.Basic import Mathlib.RingTheory.NonUnitalSubsemiring.Basic import Mathlib.Algebra.S...
Imo2019Q2.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.Angle.Sphere import Mathlib.Geometry.Euclidean.Sphere.SecondInter /-! # IMO 2019 Q2 In triangle `ABC`, point `A₁` lies on side `BC` an...
Rel.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.Set.BooleanAlgebra /-! # Relations as sets of pairs This file provides API to regard relations between `α` and `β` as sets of pairs `Set (α × β)`...
Limits.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Johan Commelin -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Limits.Creates /-! # Adjunctions and limits A left adjoint preserves colimits...
StarRingHom.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Algebra.Star.Basic /-! # Morphisms of star rings This file defines a new type of morphism between (non-unita...
Basic.lean
/- Copyright (c) 2016 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Data.Set.Defs import Mathlib.Logic.Basic import Mathlib.Logic.ExistsUnique import Mathlib.Logic.Nonempty import Mathlib.Logic.Nontrivia...
Integral.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.GroupWithZero.NonZeroDivisors import Mathlib.Algebra.Polynomial.Lifts import Mathlib.Ring...
Basic.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Johan Commelin, Bhavik Mehta -/ import Mathlib.CategoryTheory.Equivalence import Mathlib.CategoryTheory.Yoneda /-! # Adjunctions between functors `F ⊣ G` represents the dat...
Basic.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.NonUnitalNonAssocAlgebra import Mathlib.Algebra.Lie.OfAssociative import Mathlib.Algebra.Lie.Subalgebra import Mathlib.RingTheory.Nilpo...
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...
AffineTransitionLimit.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.AlgebraicGeometry.IdealSheaf.Functorial import Mathlib.AlgebraicGeometry.Morphisms.Separated import Mathlib.CategoryTheory.Filtered.Final /-! # Inverse lim...
Prod.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.Prod import Mathlib.RingTheory.Finiteness.Defs /-! # Finitely generated product (sub)modules -/ open Function (Surjective) open Finsup...
all.v
From mathcomp Require Export all_boot. From mathcomp Require Export all_order. From mathcomp Require Export all_fingroup. From mathcomp Require Export all_algebra. From mathcomp Require Export all_solvable. From mathcomp Require Export all_field. From mathcomp Require Export all_character.
SpecialLinearGroup.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Wen Yang -/ import Mathlib.LinearAlgebra.Matrix.Adjugate import Mathlib.LinearAlgebra.Matrix.ToLin import Mathlib.LinearAlgebra.Matrix.Transvection import Mathlib.RingTheory....
SemiNormedGrp.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Riccardo Brasca -/ import Mathlib.Analysis.Normed.Group.Constructions import Mathlib.Analysis.Normed.Group.Hom import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms...
polyXY.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype tuple fi...
Find.lean
import Mathlib.Tactic.Find theorem add_comm_zero {n} : 0 + n = n + 0 := Nat.add_comm _ _ -- These results are too volatile to test with `#guard_msgs`, -- we just suppress them for now. #guard_msgs (drop info) in #find _ + _ = _ + _ #guard_msgs (drop info) in #find ?n + _ = _ + ?n #guard_msgs (drop info) in #find (_...
generic_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 choice. From mathcomp Require Import seq fintype. (*****...
FiniteInfinite.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau -/ import Mathlib.Data.DFinsupp.Defs import Mathlib.Data.Fintype.Pi /-! # Finiteness and infiniteness of the `DFinsupp` type ## Main results * `DFinsupp.fintype...
Homogeneous.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Eric Wieser -/ import Mathlib.Algebra.DirectSum.Internal import Mathlib.Algebra.GradedMonoid import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Algebra.MvPolyn...
NReflectsIso.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.FunctorN import Mathlib.AlgebraicTopology.DoldKan.Decomposition import Mathlib.CategoryTheory.Idempotents.HomologicalComplex import Mat...
Finiteness.lean
/- Copyright (c) 2023 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Tactic.Positivity.Core /-! # Finiteness tactic This file implements a basic `finiteness` tactic, designed to solve goals of the form `*** < ∞` and ...
Basic.lean
/- Copyright (c) 2025 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson, Jun Kwon -/ import Mathlib.Data.Set.Basic import Mathlib.Data.Sym.Sym2 /-! # Multigraphs A multigraph is a set of vertices and a set of edges, together with incidence dat...
WithDensity.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap import Mathlib.Probability.Kernel.MeasurableLIntegral /-! # With Density For an s-finite kernel `κ : K...
Init.lean
/- Copyright (c) 2023 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Mathlib.Init import Aesop /-! # Continuity Rule Set This module defines the `Continuous` Aesop rule set which is used by the `continuity` tactic. Aesop rule...
NthRewrite.lean
import Mathlib.Tactic.NthRewrite import Mathlib.Algebra.Group.Defs import Mathlib.Data.Vector.Defs import Mathlib.Algebra.Ring.Nat set_option autoImplicit true open Mathlib example [AddZeroClass G] {a : G} (h : a = a): a = (a + 0) := by nth_rewrite 2 [← add_zero a] at h exact h example [AddZeroClass G] {a : G} ...
Wallis.lean
/- Copyright (c) 2021 Hanting Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hanting Zhang -/ import Mathlib.Analysis.SpecialFunctions.Integrals.Basic /-! # The Wallis formula for Pi This file establishes the Wallis product for `π` (`Real.tendsto_prod_pi_div_t...
ContinuousMap.lean
/- Copyright (c) 2025 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.ContinuousMap.Compact import Mathlib.Topology.ContinuousMap.Algebra import Mathlib.MeasureTheory.Integral.IntegrableOn /-! # Specific res...
algebraics_fundamentals.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 ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Block.lean
/- Copyright (c) 2018 Ellen Arlt. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin -/ import Mathlib.Data.Matrix.Basic import Mathlib.Data.Matrix.Composition import Mathlib.Data.Matrix.ConjTranspose /-!...
finset_builder.lean
import Mathlib.Order.Interval.Finset.Basic /-! # Examples of finset builder notation -/ open Finset variable {α : Type*} (p : α → Prop) [DecidablePred p] /-! ## `Data.Finset.Basic` -/ example (s : Finset α) : {x ∈ s | p x} = s.filter p := rfl /-! ## `Data.Fintype.Basic` -/ section Fintype variable [Fintype α] e...
Sinc.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.Analysis.SpecialFunctions.Trigonometric.Sinc import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic import Mathlib.MeasureTheory.Function.L1Space.Int...
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...
Rfl.lean
/- Copyright (c) 2022 Newell Jensen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Newell Jensen -/ import Mathlib.Init import Lean.Meta.Tactic.Rfl /-! # `Lean.MVarId.liftReflToEq` Convert a goal of the form `x ~ y` into the form `x = y`, where `~` is a reflexive re...
falgebra.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 div...
HasLaw.lean
/- Copyright (c) 2025 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: EtienneMarion -/ import Mathlib.Probability.Density import Mathlib.Probability.Moments.Variance /-! # Law of a random variable We introduce a predicate `HasLaw X μ P` stating that th...
Defs.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot -/ import Mathlib.Algebra.Group.Defs import Mathlib.Order.Filter.Tendsto import Mathlib.Tactic.Monotonicity.Basic import Mathlib.Topology...
Monovary.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.Data.Set.Operations import Mathlib.Order.Lattice /-! # Monovariance of functions Two functions *vary together* if a strict change in the first implies a ...
LineGraph.lean
/- Copyright (c) 2024 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Combinatorics.SimpleGraph.Basic /-! # LineGraph ## Main definitions * `SimpleGraph.lineGraph` is the line graph of a simple graph `G`, with vertices as ...
Bounded.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.GroupTheory.GroupAction.Pointwise import Mathlib.Analysis.LocallyConvex.Basic import Mathlib.Analysis.LocallyConvex.BalancedCoreHull import Mathlib.Analysis....
Units.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 /-! # Lemmas about units in `ℤ`, which interact with the order structure. -/ namespace Int theorem isUnit_iff_abs_eq {x : ℤ} :...
GodelBetaFunction.lean
/- Copyright (c) 2023 Shogo Saito. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Shogo Saito. Adapted for mathlib by Hunter Monroe -/ import Mathlib.Data.Nat.ModEq import Mathlib.Data.Nat.ChineseRemainder import Mathlib.Data.Nat.Prime.Defs import Mathlib.Data.Nat.Pai...
Invertible.lean
/- Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Robert Y. Lewis -/ import Mathlib.Algebra.MvPolynomial.Basic import Mathlib.RingTheory.AlgebraTower /-! # Invertible polynomials This file is a stub ...
DoubleFactorial.lean
/- Copyright (c) 2023 Jake Levinson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jake Levinson -/ import Mathlib.Data.Nat.Factorial.Basic import Mathlib.Tactic.Ring import Mathlib.Tactic.Positivity.Core import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # D...
Action.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Algebra.GroupWithZero.Action.Defs import Mathlib.Algebra.Order.Group.Multiset import Mathlib.Data.Finset....
Derivation.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.MvPolynomial.Supported import Mathlib.RingTheory.Derivation.Basic /-! # Derivations of multivariate polynomials In this file we prove that ...
Inv.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.Deriv.Mul import Mathlib.Analysis.Calculus.Deriv.Comp /-! # Derivatives of `x ↦ x⁻¹` and `f x / g x` In this...
Fibration.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Order.UpperLower.Basic /-! # Upper/lower sets and fibrations -/ open Set namespace Relation variable {α β : Type*} {f : α → β...
ReflectsPrecoherent.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.EffectiveEpi.Enough import Mathlib.CategoryTheory.EffectiveEpi.Preserves import Mathlib.CategoryTheory.Sites.Coherent.CoherentTopolo...
SymmDiff.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.Order.BooleanAlgebra.Set import Mathlib.Order.SymmDiff /-! # Symmetric differences of sets -/ assert_not_exists RelIso namespace Se...
Pow.lean
/- Copyright (c) 2015 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis, Yury Kudryashov -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual import Mathlib.Tactic.Lift...
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...
Defs.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro, Anne Baanen -/ import Mathlib.LinearAlgebra.Quotient.Defs import Mathlib.RingTheory.Congruence.Defs import Mathlib.RingTheory.Ideal.Defs /-! # Idea...
SurjectiveOnStalks.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties import Mathlib.RingTheory.RingHom.Surjective import Mathlib.RingTheory.Spectrum.Prime.TensorProduct import Math...
EpiMono.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.EpiMono import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi import Mathlib.CategoryTheory.LiftingProperties.Adjunction /-! # Preservati...
countalg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ss...
Defs.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.Group.Basic import Mathlib.Algebra.Order.Monoid.Unbundled.Basic import Mathlib.Order.Lattice /-! # Ordered Subtraction This file proves l...
frobenius.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 div. From mathcomp Require Import fintype bigop prime finset fingroup morphism. From mathcom...