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Cat.lean
/- Copyright (c) 2024 Nicolas Rolland. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolas Rolland -/ import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic /-! # Chosen finite products in `Cat` This file proves that the cartesian product of a pair of categories ag...
Principal.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.RingTheory.PrincipalIdealDomain import Mathlib.RingTheory.SimpleRing.Field import Mathlib.RingTheory.TwoSidedIdeal.Operations /-! # A commutative s...
OnePointEquiv.lean
/- Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bjørn Kjos-Hanssen, Oliver Nash -/ import Mathlib.Topology.Compactification.OnePoint.ProjectiveLine deprecated_module (since := "2025-06-04")
ring_compare.lean
import Mathlib.Tactic.NormNum.OfScientific import Mathlib.Tactic.Ring.Compare import Mathlib.Tactic.Ring.RingNF open Lean Elab Tactic elab "ring_le" : tactic => liftMetaFinishingTactic Mathlib.Tactic.Ring.proveLE elab "ring_lt" : tactic => liftMetaFinishingTactic Mathlib.Tactic.Ring.proveLT section Nat variable {x y...
finfield.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype div tupl...
Bundled.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather -/ import Mathlib.Init import Batteries.Tactic.Lint.Misc /-! # Bundled types `Bundled c` provides a uniform structure for bundli...
AtPrime.lean
import Mathlib.RingTheory.Localization.AtPrime.Basic deprecated_module (since := "2025-08-01")
Family.lean
/- Copyright (c) 2017 Johannes Hölzl. 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.UnivLE import Mathlib.SetTheory.Ordinal.Arithmetic /-! # Arithmetic on families of or...
Shrink.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.Logic.Small.Defs import Mathlib.Topology.Defs.Induced import Mathlib.Topology.Homeomorph.Defs /-! # Topological space structure on `Shrink X` -/ ...
Functor.lean
/- Copyright (c) 2017 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Mathlib.Tactic.Attr.Register import Mathlib.Data.Set.Defs import Mathlib.Tactic.TypeStar import Batteries.Tactic.Lint /-! # Functors This module provides additiona...
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...
choice.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (**************************************************...
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...
Basic.lean
/- Copyright (c) 2019 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.Analysis.Calculus.ContDiff.Defs import Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno import Mathlib.Analysis.Calculus.FDeriv.Ad...
EpiMono.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.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono import Mathlib.CategoryTheory.Limits.Preserves.Shapes...
ContMDiffMap.lean
/- Copyright (c) 2020 Nicolò Cavalleri. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nicolò Cavalleri -/ import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace /-! # `C^n` bundled maps In this file we define the type `ContMDiffMap` of `n` times continuously differe...
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.
Star.lean
/- Copyright (c) 2023 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Algebra.Order.Ring.Defs import Mathlib.Algebra.Order.Star.Basic /-! # Commutative star-ordered rings are ordered rings A noncommutative star-ordered ri...
ssrint.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 seq. From mathcomp Require Import fintype finfun b...
Defs.lean
/- Copyright (c) 2018 Louis Carlin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Louis Carlin, Mario Carneiro -/ import Mathlib.Algebra.Ring.Defs import Mathlib.Order.RelClasses /-! # Euclidean domains This file introduces Euclidean domains and provides the extende...
Basic.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.Algebra.Ring.Action.Basic import Mathlib.GroupTheory.Congruence.Basic import Mathlib.RingTheory.Congruence.Defs /-! # Congruence relations on rings This fi...
Span.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Chris Hughes, Mario Carneiro -/ import Mathlib.Algebra.GroupWithZero.Associated import Mathlib.Algebra.Ring.Idempotent import Mathlib.Algebra.Ring.Regular import Mathlib.LinearAl...
IsBoundedDefault.lean
import Mathlib.Data.EReal.Basic import Mathlib.Order.LiminfLimsup open Filter variable {α : Type*} {f : Filter α} {u v : α → EReal} (h : u ≤ᶠ[f] v) -- proof term example : limsup u f ≤ limsup v f := limsup_le_limsup h -- exact example : limsup u f ≤ limsup v f := by exact limsup_le_limsup h -- apply example : limsu...
Affine.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.LinearAlgebra.AffineSpace.AffineMap import Mathlib.Topology.Algebra.MulAction import Mathlib.Topology.Algebra.Group.Defs /-! # Topological propertie...
CompTypeclasses.lean
/- Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.Logic.Function.Defs /-! # Propositional typeclasses on several maps This file contains typeclasses that are used in the definition of ...
DotProduct.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen -/ import Mathlib.Algebra.Order.Star.Basic import Mathlib.Data.Matrix.RowCol import Mathlib.Algebra.Star.Pi /-! # Dot product ...
TypeStar.lean
/- Copyright (c) 2023 Matthew Robert Ballard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Init import Lean.Elab.Term /-! # Support for `Sort*` and `Type*`. These elaborate as `Sort u` and `Type u` with a fresh implicit universe variab...
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. (******************************************...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
fraction.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq. From mathcomp Require Import ssrAC choice tuple ...
Order.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.Basic /-! # Order structures and monotonicity lemmas for `Set` -/ open Function universe u v namespace Set variable {α :...
Says.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init import Lean.Meta.Tactic.TryThis import Batteries.Linter.UnreachableTactic import Qq.Match /-! # The `says` tactic combinator. If you write `X says`,...
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...
Span.lean
/- Copyright (c) 2024 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.Normed.Operator.LinearIsometry import Mathlib.Analysis.Normed.Operator.ContinuousLinearMap import Mathlib.Analysis.Normed.Module.Basic import Mathl...
finfield.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype div tupl...
test_intro_rw.v
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Lemma test_dup1 : forall n : nat, odd n. Proof. move=> /[dup] m n; suff: odd n by []. Abort. Lemma test_dup2 : let n := 1 in False. Proof. move=> /[dup] m n; have : m = n :=...
MeasurePreserving.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johannes Hölzl -/ import Mathlib.Dynamics.Ergodic.MeasurePreserving import Mathlib.MeasureTheory.Integral.Lebesgue.Basic deprecated_module (since := "2025-04-15")
Set.lean
/- Copyright (c) 2022 Ian Benway. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ian Benway -/ import Mathlib.Init import Lean.Elab.Tactic.ElabTerm /-! # The `set` tactic This file defines the `set` tactic and its variant `set!`. `set a := t with h` is a variant of ...
CircleTransform.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Data.Complex.Basic import Mathlib.MeasureTheory.Integral.CircleIntegral /-! # Circle integral transform In this file we define the circle integral tr...
Lindelof.lean
/- Copyright (c) 2023 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Topology.Bases import Mathlib.Order.Filter.CountableInter import Mathlib.Topology.Compactness.SigmaCompact /-! # Lindelöf sets and Lindelöf spaces ## Mai...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn -/ import Mathlib.Algebra.Order.SuccPred import Mathlib.Data.Sum.Order import Mathlib.SetTheory.Cardinal.Basic import Mathlib.Tactic.PPWithUniv /-! # ...
Unique.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.MeasureTheory.Function.LocallyIntegrable import Mathlib.MeasureTheory.Group.Integral import Mathlib.MeasureTheory.Integral.Prod import Mathlib.Me...
MetricSeparated.lean
/- Copyright (c) 2021 Yury Kudryashov, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Yaël Dillies -/ import Mathlib.Topology.EMetricSpace.Defs /-! # Metric separation This file defines a few notions of separations of sets in a metric s...
IsSimpleOrder.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.LinearAlgebra.FiniteDimensional.Basic import Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition import Mathlib.LinearAlgebra.FreeModule.StrongRankConditi...
Classification.lean
/- Copyright (c) 2022 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Algebra.ZMod import Mathlib.Algebra.Field.ZMod import Mathlib.Algebra.MvPolynomial.Cardinal import Mathlib.FieldTheory.IsAlgClosed.Basic import Mat...
Over.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.CategoryTheory.Monoidal.Cartesian.Basic import Mathlib.CategoryTheory.Limits.Constructions.Over.Products /-! # `CartesianMonoidalCategory` for `Over X` We...
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.Group.Basic import Mathlib.Algebra.NeZero import Mathlib.Data.Nat.Cast.Defs import Mathlib.Data.Fin.Rev /-! # Fin is a group This file cont...
seq.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. (******************************************************...
extraspecial.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 div. From mathcomp Require Import choice fintype bigop finset prime binomial. From mathc...
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...
Nucleus.lean
/- Copyright (c) 2024 Christian Krause. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chriara Cimino, Christian Krause -/ import Mathlib.Order.Closure import Mathlib.Order.Hom.CompleteLattice /-! # Nucleus Locales are the dual concept to frames. Locale theory is a b...
Image.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, Johannes Hölzl, Mario Carneiro -/ import Mathlib.Data.Set.Lattice import Mathlib.Tactic.Monotonicity.Attr /-! # The set lattice and (pre)images of fun...
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.
FiniteDimensionalLaws.lean
/- Copyright (c) 2025 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Jonas Bayer -/ import Mathlib.MeasureTheory.Constructions.Projective import Mathlib.Probability.IdentDistrib /-! # Finite dimensional distributions of a stochastic proces...
ENNReal.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.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable import Mathlib.MeasureTheory.Integral.Lebesgue.Add /-! # Finitely strongly measurable func...
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...
WithDensity.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.MeasureTheory.Integral.Lebesgue.Countable import Mathlib.MeasureTheory.Measure.Decomposition.Exhaustion import Mathlib.MeasureTheory.Gr...
Lattice.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Data.Nat.Lattice import Mathlib.Data.ENat.Basic /-! # Extended natural numbers form a complete linear order...
Prefunctor.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn, Kim Morrison -/ import Mathlib.Combinatorics.Quiver.Basic /-! # Morphisms of quivers -/ universe v₁ v₂ u u₁ u₂ /-- A morphism of quivers. As we will later have categorical f...
Basic.lean
/- Copyright (c) 2020 Gihan Marasingha. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Gihan Marasingha -/ import Mathlib.Tactic.Linarith /-! # An MIU Decision Procedure in Lean The [MIU formal system](https://en.wikipedia.org/wiki/MU_puzzle) was introduced by Dougla...
NormedSpace.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.Analysis.Normed.Module.Span import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear import Mathlib.Analysis.NormedS...
path.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. (******************************************************************************) (* ...
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...
AlexDisc.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Topology.Specialization /-! # Category of Alexandrov-discrete topological spaces This defines `AlexDisc`, the category of Alexandrov-discrete topological...
NoetherNormalization.lean
/- Copyright (c) 2025 Sihan Su. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca, Sihan Su, Wan Lin, Xiaoyang Su -/ import Mathlib.Algebra.MvPolynomial.Monad import Mathlib.Data.List.Indexes import Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basi...
MeasurableLIntegral.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.MeasurableSpace.Prod import Mathlib.Probability.Kernel.Basic /-! # Measurability of the integral against a kernel The Lebesgue integral of ...
Finset.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Data.Finset.Density import Mathlib.Tactic.NormNum.Basic import Mathlib.Tactic.Positivity.Core /-! #...
Rify.lean
import Mathlib.Tactic.Linarith import Mathlib.Tactic.Rify set_option linter.unusedVariables false example {n : ℕ} {k : ℤ} (hn : 8 ≤ n) (hk : 2 * k ≤ n + 2) : (0 : ℝ) < n - k - 1 := by rify at hn hk linarith example {n : ℕ} {k : ℤ} (hn : 8 ≤ n) (hk : (2 : ℚ) * k ≤ n + 2) : (0 : ℝ) < n - k - 1 := by rify...
EraseLead.lean
/- Copyright (c) 2020 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Alex Meiburg -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.Algebra.Polynomial.Degree.Monomial /-! # Erase the...
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 -/ import Mathlib.Data.Fin.VecNotation import Mathlib.Logic.Embedding.Set import Mathlib.Logic.Equiv.Option import Mathlib.Data.Int.Init /-! # Equivalences for `Fin n` -/ assert...
OneVariable.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction /-! # Jacobi's theta function This fil...
Constructions.lean
/- Copyright (c) 2023 Geoffrey Irving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler, Geoffrey Irving, Stefan Kebekus -/ import Mathlib.Analysis.Analytic.Composition import Mathlib.Analysis.Analytic.Linear import Mathlib.Analysis.NormedSpace.OperatorNor...
burnside_app.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 tupl...
Multiset.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.Order.Group.Finset import Mathlib.Data.Finsupp.Basic import Mathlib.Data.Sym.Basic import Mathlib.Order.Preorder.Finsupp /-! # Equivalence bet...
closed_field.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 generic_...
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********************************************************...
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...
Defs.lean
/- Copyright (c) 2017 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Johannes Hölzl, Chris Hughes, Jens Wagemaker, Jon Eugster -/ import Mathlib.Algebra.Group.Commute.Defs /-! # Units (i.e., invertible elements) of a monoid An el...
bigop.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 fintype tuple ...
WeakOperatorTopology.lean
/- Copyright (c) 2024 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.InnerProductSpace.Dual import Mathlib.Analysis.LocallyConvex.WeakOperatorTopology /-! # The weak operator topology in Hilbert spaces This...
LocalClosure.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.Basic /-! # Local closure of morphism properties We define the source local closure of a property `P` wrt. a morphism...
Pullbacks.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, Andrew Yang -/ import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback import Mathlib.CategoryTheory.Limits.Preserves.Basic import Mathlib.CategoryTheory.Limits.Op...
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 -/ import Mathlib.Control.Combinators import Mathlib.Logic.Function.Defs import Mathlib.Tactic.CasesM import Mathlib.Tactic.Attr.Core /-! Extends the theory on functors...
closed_field.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 generic_...
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...
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...
Variable.lean
import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Ring.Regular import Mathlib.Algebra.Module.LinearMap.Basic import Mathlib.RingTheory.UniqueFactorizationDomain.Basic import Mathlib.Tactic.Variable set_option autoImplicit true namespace Tests...
Operations.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Johannes Hölzl, Reid Barton, Kim Morrison, Patrick Massot, Kyle Miller, Minchao Wu, Yury Kudryashov, Floris van Doorn -/ import Mathlib.Data.Set.CoeSort import Mathlib.Da...
numdomain.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
ReImTopology.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Complex.Basic import Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle /-! # Closure, interior, and frontier of preimages under `re`...
ring_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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
ValuativeRel.lean
/- Copyright (c) 2025 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.RingTheory.Valuation.ValuativeRel import Mathlib.Topology.Algebra.Valued.ValuationTopology import Mathlib.Topology.Algebra.WithZeroTopology /-! # V...
ring_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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
TransferInstance.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.Equiv.Defs import Mathlib.Algebra.Group.InjSurj import Mathlib.Data.Fintype.Basic /-! # Transfer algebraic structures across `Equiv`s I...
Defs.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.LinearAlgebra.Basis.VectorSpace import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.RingTheory.SimpleRing.Basic /-! # Finite dimensional vector spa...
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...
Lemmas.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Joey van Langen, Casper Putz -/ import Mathlib.Algebra.CharP.Defs import Mathlib.Data.Nat.Multiplicity import Mathlib.Data.Nat.Choose.Sum /-! # Characteristic of semirings -/ a...
Hom.lean
/- Copyright (c) 2018 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Chris Hughes, Kevin Buzzard -/ import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.Hom.Basic import Mathlib.Algebra.Group.Units.Basic /-! # Monoid hom...
Positivity.lean
import Mathlib.Tactic.Positivity.Basic import Mathlib.Tactic.Positivity.Finset import Mathlib.Tactic.NormNum.Basic import Mathlib.Data.Int.Order.Basic
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...