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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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.Mod...
sylow.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 fintype prime bigop finset fingroup morphism. From mat...
PID.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.LinearAlgebra.Trace import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.LinearAlgebra.FreeModule.Finite.Basic /-! # Linear maps of modules with coeff...
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 -/ import Mathlib.SetTheory.Cardinal.Finite import Mathlib.Topology.Algebra.InfiniteSum.Basic import Mathlib.Topology.UniformSpace.Cauchy import Mathlib.Topology.Algebra...
Biproducts.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.Limits.Shapes.BinaryBiproducts import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero /-! # Preservation of biproducts We define the...
Idempotent.lean
/- Copyright (c) 2022 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Algebra.Group.Units.Defs imp...
Projection.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Manuel Candales -/ import Mathlib.Analysis.InnerProductSpace.Projection.Submodule import Mathlib.Analysis.InnerProductSpace.Projection.Reflection import Mathlib.Analysis.No...
Defs.lean
/- Copyright (c) 2024 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Algebra.Algebra.Defs /-! # Invariant Extensions of Rings Given an extension of rings `B/A` and an action of `G` on `B`, we introduce a predicate `A...
Notation.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.DFinsupp.Defs import Mathlib.Data.Finsupp.Notation /-! # Notation for `DFinsupp` This file extends the existing `fun₀ | 3 => a | 7 => b` notation to w...
Slope.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Malo Jaffré -/ import Mathlib.Analysis.Convex.Function import Mathlib.Tactic.AdaptationNote import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith /-! # Slop...
Basic.lean
/- Copyright (c) 2017 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tim Baumann, Stephen Morgan, Kim Morrison -/ import Mathlib.CategoryTheory.Category.Basic import Mathlib.Combinatorics.Quiver.Prefunctor import Mathlib.Tactic.CategoryTheory.CheckComposi...
Reassoc.lean
import Mathlib.Tactic.CategoryTheory.IsoReassoc open CategoryTheory namespace Tests.Reassoc universe v₁ v₂ v₃ u₁ u₂ u₃ variable {C : Type u₁} {D : Type u₂} {E : Type u₃} [Category.{v₁} C] [Category.{v₂} D] [Category.{v₃} E] {F : C ⥤ D} {G : D ⥤ E} @[reassoc] lemma foo {x y z : C} (f : x ⟶ y) (g : y ⟶ z) (h : x ...
Isomorphisms.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, Kevin Buzzard, Yury Kudryashov -/ import Mathlib.LinearAlgebra.Quotient.Basic import Mathlib.LinearAlgebra.Quotient.Card /-! # Isomorphism theorems for...
intdiv.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 div choice fintype...
ImplicitUniverses.lean
import Mathlib.Tactic.TypeStar import Mathlib.Tactic.SuccessIfFailWithMsg /-- error: Type mismatch _y has type Type u_2 of sort `Type (u_2 + 1)` but is expected to have type Type u_1 of sort `Type (u_1 + 1)` -/ #guard_msgs in noncomputable example (_x _y : Type*) : sorry := by exact _x = _y /-- error: Type mi...
Subcategory.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.Localization.CalculusOfFractions import Mathlib.CategoryTheory.Localization.Triangulated import Mathlib.CategoryTheory.ObjectProperty.ContainsZero...
Tannaka.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.ModuleCat.Basic import Mathlib.LinearAlgebra.Span.Basic /-! # Tannaka duality for rings A ring `R` is equivalent to the endomorphisms of...
Completion.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis -/ import Mathlib.Analysis.InnerProductSpace.LinearMap import Mathlib.Analysis.Normed.Module.Completion /-! # Completion of an inner p...
Const.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Bhavik Mehta -/ import Mathlib.CategoryTheory.Opposites /-! # The constant functor `const J : C ⥤ (J ⥤ C)` is the functor that sends an object `X : C` to the functor `J ⥤...
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...
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. (**************************************************...
Order.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Jeremy Avigad, Floris van Doorn -/ import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic import Mathlib.Order.RelClasses /-! # Deprecated instances abou...
Finset.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.Fin.Tuple import Mathlib.Order.Hom.Set import Mathlib.Data.Finset.Insert /-! # Order isomorphisms from Fin to finsets We define order isomorphisms like `...
choose.lean
import Batteries.Util.ExtendedBinder import Mathlib.Tactic.Choose /-! # Tests for the `choose` tactic -/ set_option autoImplicit true example {α : Type} (h : ∀ n m : α, ∀ (h : n = m), ∃ i j : α, i ≠ j ∧ h = h) : True := by choose! i j _x _y using h trivial example (h : ∀ n m : Nat, ∃ i j, m = n + i ∨ m + j = n)...
Basic.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Topology.UniformSpace.UniformConvergence import Mathlib.Topology.UniformSpace.UniformEmbedding import Mathlib.Topology.UniformSpace.Com...
Order.lean
/- Copyright (c) 2021 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Algebra.Module.Submodule.Defs import Mathlib.Algebra.Order.Monoid.Basic /-! # Ordered instances on submodules -/ namespace Submodule variable {R M : Ty...
TermReduce.lean
/- Copyright (c) 2023 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Gabriel Ebner, Yuyang Zhao -/ import Lean.Meta.Tactic.Delta import Mathlib.Lean.Expr.Basic /-! # Term elaborators for reduction -/ namespace Mathlib.Util.TermReduce open L...
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...
cyclotomic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
ProperlyDiscontinuous.lean
/- Copyright (c) 2024 Anatole Dedeker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Topology.Algebra.ProperAction.Basic import Mathlib.Topology.Maps.Proper.CompactlyGenerated /-! # When a proper action is properly discontinuous This...
Fraisse.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Gabin Kolly -/ import Mathlib.ModelTheory.FinitelyGenerated import Mathlib.ModelTheory.PartialEquiv import Mathlib.ModelTheory.Bundled import Mathlib.Algebra.Order.Arch...
ordered_ring.lean
import Mathlib.Algebra.Order.Ring.Defs example {K : Type _} [CommRing K] [PartialOrder K] [IsStrictOrderedRing K] (this : 0 ≤ (-1 : K)) : False := by grind example {K : Type _} [CommRing K] [PartialOrder K] [IsStrictOrderedRing K] (this : 0 ≤ (-c - 1) + c) : b * b - 4 * 0 * c ≤ 0 := by grind
OreSet.lean
/- Copyright (c) 2022 Jakob von Raumer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob von Raumer, Kevin Klinge -/ import Mathlib.Algebra.Group.Submonoid.Defs /-! # (Left) Ore sets This defines left Ore sets on arbitrary monoids. ## References * https://ncat...
Bernstein.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.MvPolynomial.PDeriv import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative import Mathlib.Algebra.Polynomial.Eva...
Defs.lean
/- Copyright (c) 2021 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino, Floris van Doorn -/ import Mathlib.Init /-! ## Definitions on Arrays This file contains various definitions on `Array`. It does not contain proofs about these defin...
all_fingroup.v
From mathcomp Require Export action. From mathcomp Require Export automorphism. From mathcomp Require Export fingroup. From mathcomp Require Export gproduct. From mathcomp Require Export morphism. From mathcomp Require Export perm. From mathcomp Require Export presentation. From mathcomp Require Export quotient.
JordanHolder.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Order.Lattice import Mathlib.Data.List.Sort import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Logic.Equiv.Functor import Mathlib.Data.Fintype.Pigeonhole ...
Adjunction.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.Category.Cat import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.ConnectedComponents /-! # Adjunctions relat...
Defs.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot, Eric Wieser -/ import Mathlib.Algebra.Notation.Defs import Mathlib.Util.AssertExists /-! # Notation for algebraic operators on pi types This file provides o...
Matrix.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Data.Matrix.Kronecker import Mathlib.LinearAlgebra.Matrix.ToLin import Mathlib.LinearAlgebra.TensorProduct.Basis /-! # Connections between `TensorProduct` a...
PartitionOfUnity.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.BigOperators.Finprod import Mathlib.Topology.ContinuousMap.Algebra import Mathlib.Topology.Compactness.Paracompact import Mathlib.Topology.Sh...
PUnit.lean
/- Copyright (c) 2022 Praneeth Kolichala. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Praneeth Kolichala -/ import Mathlib.CategoryTheory.PUnit import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic /-! # Fundamental groupoid of punit The fundamental groupoid ...
ExtremallyDisconnected.lean
/- Copyright (c) 2021 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Topology.Homeomorph.Lemmas import Mathlib.Topology.Compactification.StoneCech /-! # Extremally disconnected spaces An extremally disconnected topolog...
Seminorm.lean
/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Yaël Dillies, Moritz Doll -/ import Mathlib.Algebra.Order.Pi import Mathlib.Analysis.Convex.Function import Mathlib.Analysis.LocallyConvex.Basic import Mathlib.Data.Real.Pointwise /...
TwoPointing.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.Logic.Nontrivial.Defs import Mathlib.Logic.Nonempty import Mathlib.Tactic.Simps.Basic /-! # Two-pointings This file defines `TwoPointing α`, the type of ...
AddCircleAdd.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.Dynamics.Ergodic.Action.OfMinimal import Mathlib.Topology.Instances.AddCircle.DenseSubgroup import Mathlib.MeasureTheory.Integral.IntervalIntegral.Pe...
Adjunctions.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Johannes Hölzl, Andrew Yang -/ import Mathlib.Algebra.Category.Ring.Colimits import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.CategoryTheory.Comma.Over.Basic imp...
Finset.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Pointwise.Finset.Scalar import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Group.Pointwise.Finset.Basic /-! # Pointwise actions on se...
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...
Submodule.lean
/- Copyright (c) 2021 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Eric Wieser -/ import Mathlib.RingTheory.GradedAlgebra.Basic import Mathlib.Algebra.GradedMulAction /-! # Homogeneous submodules of a graded module This file defines homo...
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...
Isaacs.lean
/- Copyright (c) 2024 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.FieldTheory.Normal.Basic import Mathlib.FieldTheory.PrimitiveElement import Mathlib.GroupTheory.CosetCover /-! # Algebraic extensions are determined by their se...
Constructions.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.Order.Filter.AtTopBot.Finset import Mathlib.Topology.Algebra.InfiniteSum.Group import Mathlib.Topology.Algebra.Star /-! # Topological sums and functor...
center.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 fintype bigop finset fingroup morphism perm. From math...
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. (**************************************************...
Subterminal.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.Terminal import Mathlib.CategoryTheory.Subobject.MonoOver /-! # Su...
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 ...
CStarMatrix.lean
/- Copyright (c) 2025 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.CStarAlgebra.Module.Constructions import Mathlib.Analysis.Matrix import Mathlib.Topology.UniformSpace.Matrix /-! # Matrices with entries i...
CompleteSeparated.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Topology.UniformSpace.UniformEmbedding /-! # Theory of complete separated uniform spaces. This file is for elementary lemmas that depend on bot...
ClassGroup.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.DedekindDomain.Ideal.Basic /-! # The ideal class group This file defines the ideal class group `ClassGroup R` of fractional ideals of `R` inside...
GrindInstances.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.Algebra.Ring.Defs import Mathlib.Data.Int.Cast.Basic /-! # Instances for `grind`. -/ open Lean variable (α : Type*) -- This is a low priority instance...
Rank.lean
/- Copyright (c) 2022 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.RingTheory.SimpleModule.Basic /-! # A module over a division ring is simple iff it has rank one -/ theore...
Basic.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.Algebra.Field.IsField import Mathlib.Algebra.GroupWithZero.N...
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...
Functor.lean
/- Copyright (c) 2024 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel -/ import Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated import Mathlib.CategoryTheory.Adjunction.Opposites /-! # Opposites of functors between pretriangulate...
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.
AddTorsor.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Yury Kudryashov -/ import Mathlib.Analysis.Normed.Group.Submodule import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic import Mathlib.LinearAlgebra.AffineSpace.Mid...
FiniteMeasure.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.MeasureTheory.Integral.Bochner.ContinuousLinearMap import Mathlib.MeasureTheory.Measure.HasOuterApproxClosed import Mathlib.MeasureTheory.Measure.Prod impo...
Concrete.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.ConcreteCategory.Basic import Mathlib.CategoryTheory.MorphismProperty.Composition import Mathlib.CategoryTheory.MorphismProperty.Factorization...
AffineSpace.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.MvPolynomial.Monad import Mathlib.AlgebraicGeometry.Morphisms.Finite import Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation import Mathlib.Rin...
Basic.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro -/ import Mathlib.Algebra.Module.Submodule.Bilinear import Mathlib.Algebra.Module.Equiv.Basic import Mathlib.GroupTheory.Congruence.Hom import Mathlib.Tactic.Abel ...
Init.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Batteries.Tactic.Alias import Batteries.Tactic.Init import Mathlib.Init im...
LogBounds.lean
/- Copyright (c) 2023 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Complex.Convex import Mathlib.Analysis.SpecialFunctions.Integrals.Basic import Mathlib.Analysis.Calculus.Deriv.Shift /-! # Estimates for the co...
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...
TypeTags.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.Group.Int.Defs import Mathlib.Algebra.Group.TypeTags.Basic /-! # Lemmas about `Multiplicative ℤ`. -/ open Nat namespace Int section Multipli...
eqtype.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool. (********************************************************************...
SModEq.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.Algebra.Module.Submodule.Map import Mathlib.Algebra.Polynomial.Eval.Defs import Mathlib.RingTheory.Ideal.Quotient.Defs /-! # modular equivalence for submodule -...
InvariantBasisNumber.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, Kim Morrison -/ import Mathlib.RingTheory.Ideal.Quotient.Basic import Mathlib.RingTheory.Noetherian.Orzech import Mathlib.RingTheory.OrzechProperty import Mathlib.RingThe...
Ordset.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Ordmap.Invariants /-! # Verification of `Ordnode` This file uses the invariants defined in `Mathlib/Data/Ordmap/Invariants.lean` to construct `O...
Basic.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Yaël Dillies -/ import Mathlib.Algebra.Group.Pointwise.Set.Finite import Mathlib.Algebra.Group.Pointwise.Set.ListOfFn import Mathlib.Algebra.Order.Monoid.Unbundled....
AffineSubspace.lean
/- Copyright (c) 2025 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic import Mathlib.Topology.Algebra.ContinuousAffineMap /-! # Topology of affine subspaces. This file defines ...
OnePoint.lean
/- Copyright (c) 2021 Yourong Zang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yourong Zang, Yury Kudryashov -/ import Mathlib.Topology.Compactification.OnePoint.Basic deprecated_module (since := "2025-06-04")
HEval.lean
/- Copyright (c) 2024 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.RingTheory.HahnSeries.Summable import Mathlib.RingTheory.PowerSeries.Basic /-! # Evaluation of power series in Hahn Series We describe a class of rin...
Domain.lean
/- Copyright (c) 2022 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.RingTheory.WittVector.Identities /-! # Witt vectors over a domain This file builds to the proof `WittVector.instIsDomain`, an instance that says i...
HurwitzZetaEven.lean
/- Copyright (c) 2024 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.NumberTheory.LSeries.AbstractFuncEq import Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds import Mathlib.Analysis.SpecialFunctions.Gamma.Deligne ...
Noetherian.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.RingTheory.AdicCompletion.Basic import Mathlib.RingTheory.Filtration /-! # Hausdorff-ness for noetherian rings -/ open IsLocalRing variable {R : Type*} [C...
Pointwise.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.GroupWithZero.Submonoid.Pointwise import Mathlib.Algebra.Ring.Subsemiring.Basic /-! # Pointwise instances on `Subsemiring`s This file provides the ...
ApplyAt.lean
/- Copyright (c) 2023 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Lean.Elab.Tactic.ElabTerm import Mathlib.Lean.Meta.Basic /-! # Apply at A tactic for applying functions at hypotheses. -/ open Lean Meta Elab Tactic Term namespace...
PSet.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.Set.Lattice /-! # Pre-sets A pre-set is inductively defined by its indexing type and its members, which are themselves pre-sets. After defining...
Equivalence.lean
/- Copyright (c) 2025 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Equivalence of real-valued absolute values Two absolute values `v₁, v₂ : AbsoluteValue R ℝ` are *equivalent* i...
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...
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.
Presheaf.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.ModuleCat.Presheaf import Mathlib.AlgebraicGeometry.Scheme import Mathlib.CategoryTheory.Sites.Whiskering /-! # The category of presheaves of m...
FunctorOfCocone.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.SmallObject.Iteration.Basic /-! # The functor from `Set.Iic j` deduced from a cocone Given a functor `F : Set.Iio j ⥤ C` and `c : Cocone F`, we...
Lemmas.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Patrick Massot -/ import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.Hom.Instances import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Tors...
PrincipalSeg.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.InitialSeg import Mathlib.CategoryTheory.Category.Preorder import Mathlib.CategoryTheory.Limits.Cones /-! # Cocones associated to principal segments If `...
Finite.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.Integral import Mathlib.Algebra.Category.Ring.Epi /-! # Finite morphisms of schemes A morphism of schem...
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...
Lattice.lean
/- Copyright (c) 2021 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin, Yaël Dillies -/ import Mathlib.Algebra.Order.Group.OrderIso /-! # Lattice ordered groups Lattice ordered groups were introduced by [Birkhoff][birkhoff1942]. T...
OfMap.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Fintype.Defs import Mathlib.Data.Finset.Image /-! # Constructors for `Fintype` This file contains basic constructors for `Fintype` instances, gi...