filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
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... |
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