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Equivalence.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.EquivalencePseudoabelian import Mathlib.AlgebraicTopology.DoldKan.Normalized /-! # The Dold-Kan correspondence The Dold-Kan correspo...
Equivalence.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.CategoryTheory.Galois.EssSurj import Mathlib.CategoryTheory.Action.Continuous import Mathlib.Topology.Category.FinTopCat /-! # Fiber functors indu...
Basic.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.Analysis.SpecialFunctions.Pow.NNReal import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex import Mathlib.MeasureTheory.Constructions.BorelSp...
Basic.lean
/- Copyright (c) 2018 Andreas Swerdlow. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andreas Swerdlow, Kexing Ying -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.LinearAlgebra.BilinearMap /-! # Bilinear form This file defines a bilinear form over a module. ...
Expr.lean
/- Copyright (c) 2019 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Simon Hudon, Kim Morrison, Keeley Hoek, Robert Y. Lewis, Floris van Doorn -/ import Mathlib.Lean.Expr.Basic import Mathlib.Lean.Expr.ReplaceRec
gproduct.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigo...
Free.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.Algebra.Homology.ShortComplex.ModuleCat /-! # Exact sequences with free modules This file proves resu...
Defs.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.Data.Int.Cast.Defs import Mathlib.Logic.Basic /-! # Characteristic zero A ring `R` is called of characteristic zero if every natural number `n` is n...
Qq.lean
import Mathlib.Util.Qq import Mathlib.Data.Finset.Basic open Qq Lean Elab Meta section mkSetLiteralQ /-- info: {1, 2, 3} : Finset ℕ -/ #guard_msgs in #check by_elab return mkSetLiteralQ q(Finset ℕ) [q(1), q(2), q(3)] /-- info: {1, 2, 3} : Multiset ℕ -/ #guard_msgs in #check by_elab return mkSetLiteralQ q(Multiset ...
Content.lean
/- Copyright (c) 2020 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Algebra.GCDMonoid.Finset import Mathlib.Algebra.Polynomial.CancelLeads import Mathlib.Algebra.Polynomial.EraseLead import Mathlib.Algebra.Polynomial.Fi...
Group.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, Yury Kudryashov, Rémy Degenne -/ import Mathlib.Algebra.Order.Group.Abs import Mathlib.Algebra.Order.Group.Basic import Mathlib.Algebra....
AddCircle.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Analysis.Normed.Group.Quotient import Mathlib.Analysis.NormedSpace.Pointwise import Mathlib.Topology.Instances.AddCircle.Real /-! # The additive circle as a...
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...
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 ...
inertia.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...
Imo1972Q5.lean
/- Copyright (c) 2020 Ruben Van de Velde, Stanislas Polu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ruben Van de Velde, Stanislas Polu -/ import Mathlib.Data.Real.Basic import Mathlib.Analysis.Normed.Module.Basic /-! # IMO 1972 Q5 Problem: `f` and `g` are real-v...
all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
Holder.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.Data.ENNReal.Inv /-! # Hölder triples This file defines a new class: `ENNReal.HolderTriple` which takes arguments `p q r : ℝ≥0∞`, with `r` marked as a ...
Basic.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.Algebra.Category.Grp.Basic import Mathlib.Algebra.Ring.PUnit import Mathlib.CategoryTheory.Adjunction.Limits import Mathlib.CategoryTheory.Conj import Math...
Recall.lean
import Mathlib.Tactic.Recall import Mathlib.Analysis.Calculus.Deriv.Basic import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic import Mathlib.Data.Complex.Trigonometric set_option linter.style.setOption false -- Remark: When the test is run by make/CI, this option is not set, so we set it here. set_option pp.u...
mxrepresentation.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...
Equiv.lean
/- Copyright (c) 2024 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.RingTheory.Coalgebra.Equiv import Mathlib.RingTheory.Bialgebra.Hom /-! # Isomorphisms of `R`-bialgebras This file defines bundled isomorphisms ...
fingraph.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import seq path fintype. (******************************************...
Lemmas.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.LieTheorem import Mathlib.Algebra.Lie.Semisimple.Basic /-! # Lemmas about semisimple Lie algebras This file is a home for lemmas about semisimp...
EffectiveEpi.lean
/- Copyright (c) 2024 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Coherent.Comparison import Mathlib.Topology.Category.CompHausLike.Limits /-! # Effective epimorphisms in `CompHau...
IntPolynomial.lean
/- Copyright (c) 2024 María Inés de Frutos-Fernández, Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: María Inés de Frutos-Fernández, Filippo A. E. Nuccio -/ import Mathlib.Algebra.Polynomial.AlgebraMap /-! # Polynomials over subrings. Given a fi...
Locale.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.Frm import Mathlib.Topology.Category.CompHaus.Frm /-! # The category of locales This file defines `Locale`, the category of locales. This ...
PureCoherence.lean
/- Copyright (c) 2024 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Lean.Meta.Tactic.Apply import Mathlib.Tactic.CategoryTheory.Coherence.Datatypes /-! # Coherence tactic This file provides a meta framework for the coherence tactic...
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...
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...
cyclic.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 bigo...
Subobject.lean
/- Copyright (c) 2021 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.Algebra.Category.Grp.ZModuleEquivalence import Mathlib.Algebra.Category.ModuleCat.Subobject /-! # The category of abelian groups is well-powered -/ op...
Cofinality.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios -/ import Mathlib.SetTheory.Cardinal.Arithmetic import Mathlib.SetTheory.Ordinal.FixedPoint /-! # Cofinality This file co...
interval_inference.v
(* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice. From mathcomp Require Import order ssralg ssrnum ssrint interval. (**md********************************************************...
HomotopyCofiber.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomologicalComplexBiprod import Mathlib.Algebra.Homology.Homotopy import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy /-! The homotopy ...
LConvolution.lean
/- Copyright (c) 2025 David Ledvinka. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Ledvinka -/ import Mathlib.MeasureTheory.Group.Prod import Mathlib.MeasureTheory.Group.LIntegral /-! # Convolution of functions using the Lebesgue integral In this file we defi...
IrreducibleRing.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.Algebra.Polynomial.Eval.Irreducible import Mathlib.RingTheory.Polynomial.Nilpotent /-! # Polynomials over an irreducible ring This file contains results about the p...
primitive_action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat. From mathcomp Require Import div seq fintype tuple finset. From mathcomp Require Import fin...
Submodule.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Projection.Basic /-! # Subspaces associated with orthogonal projections Here, the orthogon...
l2Space.lean
/- Copyright (c) 2022 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.Projection.Basic import Mathlib.Analysis.Normed.Lp.lpSpace import Mathlib.Analysis.InnerProductSpace.PiL2 /-! # Hilbert s...
IsPrincipalPowQuotient.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.LinearAlgebra.Isomorphisms import Mathlib.RingTheory.Ideal.Operations import Mathlib.RingTheory.Ideal.Quotient.Defs /-! # Quotients of powers of pri...
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...
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.Topology.Algebra.Monoid.Defs /-! # Definitions about topological groups In this file we define mixin classes `Continu...
Linear.lean
/- Copyright (c) 2023 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.Weights.Basic import Mathlib.LinearAlgebra.Trace import Mathlib.LinearAlgebra.FreeModule.PID /-! # Lie modules with linear weights Given a Lie ...
Fubini.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.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Products.Basic import Mathlib.CategoryTheory.Functor.Currying import Mathlib.CategoryTheory.P...
State.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.SetTheory.Game.Short import Mathlib.Tactic.Linter.DeprecatedModule deprecated_module "This module is now at `CombinatorialGames.Game.ConcreteGame` in th...
LocallyDiscrete.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.Bicategory.Functor.Pseudofunctor import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete /-! # Pseudofunctors from locally discrete bicategories...
IteratedFDeriv.lean
/- Copyright (c) 2024 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.ContDiff.Operations import Mathlib.Analysis.Calculus.ContDiff.CPolynomial import Mathlib.Data.Fintype.Perm /-! # The iterated ...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
SemiconjSup.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.Group.Units.Equiv import Mathlib.Algebra.Order.Group.End import Mathlib.Logic.Function.Conjugate import Mathlib.Order.Bounds.OrderIso import ...
Membership.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard, Amelia Livingston, Yury Kudryashov -/ import Mathlib.Algebra.BigOperators.Group.Multiset.Defs import Mathlib.A...
AddCharacter.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots import Mathlib.FieldTheory.Finite.Trace import Mathlib.Algebra.Group.AddChar import Mathlib.Data.ZMod.Units import...
Grothendieck.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Calle Sönne -/ import Mathlib.CategoryTheory.Bicategory.LocallyDiscrete import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo /-! # The Grothendieck construction Given ...
gproduct.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigo...
Norm.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.Analysis.Normed.Group.Basic import Mathlib.MeasureTheory.Integral.Lebesgue.Basic /-! # Interactions between the Lebesgue integral and ...
Operations.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Algebra.Bilinear import Mathlib.Algebra.Algebra.Opposite import Mathlib.Algebra.Group.Pointwise.Finset.Basic import Mathlib.Algebra.Group.Pointwise.Set.B...
RootSystem.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.Lie.Weights.Killing import Mathlib.LinearAlgebra.RootSystem.Basic import Mathlib.LinearAlgebra.RootSystem.Irreducible import Mathlib.LinearAlgebra.Ro...
Convolution.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.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.ParametricIntegral import Mathlib.MeasureTheory.Integral.Prod import Mathlib.Meas...
ErwQuestion.lean
/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init import Lean.Elab.Tactic.Rewrite /-! # The `erw?` tactic `erw? [r, ...]` calls `erw [r, ...]` (at hypothesis `h` if written `erw [r, ...] at h`), an...
ToFinsupp.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.BigOperators.Group.List.Basic import Mathlib.Algebra.Group.Embedding import Mathlib.Algebra.Group.Finsupp import Mathlib.Algebra.Group.Nat.De...
LevelOne.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Analysis.Complex.AbsMax import Mathlib.NumberTheory.Modular import Mathlib.NumberTheory.ModularForms.QExpansion /-! # Level one modular forms This fil...
Basic.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz, Dagur Asgeirsson -/ import Mathlib.Topology.ExtremallyDisconnected import Mathlib.Topology.Category.CompHaus.Projective import Mathlib.Topology.Category.Profinite.Basic /-! # E...
Thickening.lean
/- Copyright (c) 2021 Kalle Kytölä. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kalle Kytölä -/ import Mathlib.Topology.MetricSpace.HausdorffDistance /-! # Thickenings in pseudo-metric spaces ## Main definitions * `Metric.thickening δ s`, the open thickening by ra...
Linear.lean
/- Copyright (c) 2021 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.Order.Zorn /-! # Extend a partial order to a linear order This file constructs a linear order which is an extension of the given partial order, using Zor...
Presheaf.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Joël Riou -/ import Mathlib.CategoryTheory.Comma.Presheaf.Basic import Mathlib.CategoryTheory.Elements import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction import ...
Bound.lean
/- Copyright (c) 2024 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geoffrey Irving -/ import Aesop import Mathlib.Tactic.Bound.Attribute import Mathlib.Tactic.Lemma import Mathlib.Tactic.Linarith.Frontend import Mathlib.Tactic.NormNum.Core /-! ## T...
IsAlgClosed.lean
/- Copyright (c) 2025 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.RingTheory.SimpleModule.WedderburnArtin /-! # Wedderburn–Artin Theorem over an algebraically closed field -/ varia...
Limit.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.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # The category of s...
Localization.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.Algebra.Module.LocalizedModule.IsLocalization import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.RingTheory.Ideal.Quotient.Operations impo...
rat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import prime fintype fi...
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...
Basic.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.Algebra.MvPolynomial.PDeriv import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic import Mathlib.Data.Fin.Tuple.Reflection im...
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...
CommGrp_.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.CategoryTheory.Monoidal.Cartesian.CommMon_ import Mathlib.CategoryTheory.Monoidal.Cartesian.Grp_ /-! # Yoneda embedding of `CommGrp_ C` -/ assert_not_exi...
PreorderRestrict.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Order.Restriction import Mathlib.Topology.Constructions /-! # Continuity of the restriction function for functions indexed by a preorder We prove tha...
TwoSquare.lean
/- Copyright (c) 2025 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Jakob von Raumer -/ import Mathlib.CategoryTheory.Whiskering import Mathlib.CategoryTheory.Opposites import Mathlib.Tactic.CategoryTheory.Slice /-! # 2-squares of functor...
Tree.lean
/- Copyright (c) 2024 Sven Manthe. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sven Manthe -/ import Mathlib.Order.CompleteLattice.SetLike /-! # Trees in the sense of descriptive set theory This file defines trees of depth `ω` in the sense of descriptive set theor...
PiSystem.lean
/- Copyright (c) 2021 Martin Zinkevich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Martin Zinkevich, Rémy Degenne -/ import Mathlib.Logic.Encodable.Lattice import Mathlib.MeasureTheory.MeasurableSpace.Defs import Mathlib.Order.Disjointed /-! # Indu...
Set.lean
/- Copyright (c) 2024 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Timothy Carlin-Burns -/ import Mathlib.Data.Set.Lattice import Mathlib.Logic.Small.Basic /-! # Results about `Small` on coerced sets -/ universe u u1 u2 u3 u4 variable...
Fix.lean
/- Copyright (c) 2020 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Data.Part import Mathlib.Data.Nat.Find import Mathlib.Data.Nat.Upto import Mathlib.Data.Stream.Defs import Mathlib.Tactic.Common /-! # Fixed point This mod...
SumIteratedDerivative.lean
/- Copyright (c) 2022 Yuyang Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuyang Zhao -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.Algebra.Polynomia...
UniformEmbedding.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot -/ import Mathlib.Topology.UniformSpace.Cauchy import Mathlib.Topology.UniformSpace.Separation import Mathlib.Topology.DenseEmbedding ...
Lemmas.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Shing Tak Lam, Mario Carneiro -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Algebra.BigOperators.Ring.List import Mathlib.Data.Int.ModEq import Mathlib.Da...
Imo1959Q1.lean
/- Copyright (c) 2020 Kevin Lacker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Lacker -/ import Mathlib.Tactic.Ring import Mathlib.Data.Nat.Prime.Basic /-! # IMO 1959 Q1 Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every natural number `n`. ...
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 -/ import Mathlib.Algebra.Notation.Indicator import Mathlib.Data.Int.Cast.Pi import Mathlib.Data.Nat.Cast.Basic import Mathlib.MeasureTheory.MeasurableSp...
SplitLengths.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.Algebra.Group.Nat.Defs import Mathlib.Order.MinMax /-! # Splitting a list to chunks of specified lengths This file defines splitting a list to chunks of ...
CartesianMonoidal.lean
/- Copyright (c) 2024 Robin Carlier. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robin Carlier -/ import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory import Mathlib.CategoryTheory.Sites.Limits /-! # Chosen finite products on sheaves In this file, we p...
IndexNormal.lean
/- Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Data.Finite.Perm import Mathlib.Data.Nat.Prime.Factorial import Mathlib.GroupTheory.Index /-! # Subgroups of small index are normal * `...
commutator.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 fintype. From mathcomp Require Import bigop finset binomial fingroup morphism. From mathcomp...
Prime.lean
/- Copyright (c) 2020 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Ring.Divisibility.Basic import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Prime.Defs import Mathlib.Algebra.Ring.Units import...
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.Sigma.Order import Mathlib.Order.Interval.Finset.Defs /-! # Finite intervals in a sigma type This file provides the `LocallyFiniteOrder` instance fo...
Set.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura -/ import Mathlib.Data.Set.Insert import Mathlib.Order.BooleanAlgebra.Basic /-! # Boolean algebra of sets This file proves that `Set α` is a boolean a...
NonUnitalAlgebra.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.Algebra.Algebra.NonUnitalSubalgebra import Mathlib.Topology.Algebra.Module.Basic /-! # Non-unital topological (sub)algebras A non-unital topological al...
all_ssreflect.v
Attributes deprecated(since="mathcomp 2.5.0", note="Use 'all_boot' and/or 'all_order' instead."). From mathcomp Require Export all_boot. From mathcomp Require Export preorder. From mathcomp Require Export order.
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...
Iterate.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.Logic.Function.Iterate import Mathlib.Order.Monotone.Basic /-! # Inequalities on iterates In this file we prove some inequalities comparing `f^[n] ...
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...
Fintype.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.Data.Fintype.EquivFin import Mathlib.Data.Fintype.Inv /-! # Equivalence between fintypes This file contains some basic results on equivalences wher...
Tuple.lean
/- Copyright (c) 2019 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yury Kudryashov, Sébastien Gouëzel, Chris Hughes -/ import Mathlib.Data.Fin.VecNotation import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Order.Fin.Basic import M...
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 ...