filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
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.
(******************************************************************************)
(* ... |
Basic.lean | /-
Copyright (c) 2025 Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Christian Merten, Michał Mrugała, Andrew Yang
-/
import Mathlib.Algebra.Category.AlgCat.Basic
import Mathlib.Algebra.Category... |
Basic.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.Group.Action.Basic
import Mathlib.Algebra.GroupWithZero.Action.End
import Mathlib.Algebra.Ring.Hom.Defs
/-!
# Group action on rings
This file defines t... |
OrderedSMul.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.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Invertible
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Order.Modu... |
Hadamard.lean | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Data.Matrix.Basic
/-!
# Hadamard product of matrices
This file defines the Hadamard product `Matrix.hadamard`... |
Hom.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.LinearAlgebra.RootSystem.Defs
/-!
# Morphisms of root pairings
This file defines morphisms of root pairings, following the definition of morphisms of ... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
Simple.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.RingTheory.SimpleModule.Basic
import Mathlib.Topology.Algebra.Module.Basic
/-!
# The kernel of a linear function is closed or dense
In this file ... |
MonicNonRegular.lean | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Polynomial.Monic
/-!
# `Monic` does not necessarily imply `IsRegular` in a `Semiring` with no opposites
This counterexample shows that the hyp... |
Ring.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Jeremy Avigad
-/
import Mathlib.Order.Filter.Germ.OrderedMonoid
import Mathlib.Algebra.Order.Ring.Defs
/-!
# Lemmas about filters and ordered rings.
-/
namespace Filte... |
Bousfield.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.ObjectProperty.ClosedUnderIsomorphisms
import Mathlib.CategoryTheory.MorphismProperty.Composition
import Mathlib.CategoryTheory.Localization.Adjun... |
alt.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import div fintype tupl... |
LinearMapPiProd.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import Mathlib.Topology.Algebra.Module.LinearMap
/-!
# Continuous linear maps ... |
CoreM.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
/-!
# Additional functions using `CoreM` state.
-/
open Lean Core
/--
Run a `CoreM α` in a fresh `Environment` with specified `modules : List Name`... |
Sylow.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Thomas Browning
-/
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Data.SetLike.Fintype
import Mathlib.GroupTheory.PGroup
import Mathlib.GroupTheory.NoncommPi... |
DFinsupp.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Data.DFinsupp.Submonoid
import Mathlib.Data.DFinsupp.Sigma
import Mathlib.Data.Finsupp.ToDFinsupp
import Mathlib.LinearAlgebra.Finsupp.SumProd
im... |
MonoidalComp.lean | import Mathlib.Tactic.CategoryTheory.MonoidalComp
universe v u
noncomputable section
namespace CategoryTheory
open scoped MonoidalCategory
variable {C : Type u} [Category.{v} C] [MonoidalCategory C]
example (X : C) : X ≅ (X ⊗ (𝟙_ C ⊗ 𝟙_ C)) := monoidalIso _ _
example (X1 X2 X3 X4 X5 X6 X7 X8 X9 : C) :
(𝟙_... |
HomotopyCategory.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Homology.Homotopy
import Mathlib.Algebra.Homology.Linear
import Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
import Mathlib.CategoryTheory.... |
Unbundled.lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Data.Set.Defs
import Mathlib.Tactic.ExtendDoc
import Mathlib.Tactic.Lemma
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.TypeStar
/-!
... |
Weierstrass.lean | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Analysis.SpecialFunctions.Bernstein
import Mathlib.Topology.Algebra.Algebra
import Mathlib.Topology.ContinuousMap.Compact
/-!
# The Weierstrass approximat... |
LeftRightLim.lean | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Order.LeftRight
import Mathlib.Topology.Order.Monotone
/-!
# Left and right limits
We define the (strict) left and right limits of a f... |
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.LocallyConvex.WithSeminorms
import Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual
/-!
# The weak operator topology
This file defi... |
Integrable.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral
import Mathlib.MeasureTheory.Function.LpOrder
import Mathlib.MeasureTheory.Function.StronglyMeasurable.L... |
MaxPowDiv.lean | import Mathlib.NumberTheory.Padics.PadicVal.Basic
/--
info: 100000
-/
#guard_msgs in
/- Previously this would hang -/
#eval padicValNat 2 (2 ^ 100000)
|
OrderOfVanishing.lean | /-
Copyright (c) 2025 Raphael Douglas Giles. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Raphael Douglas Giles
-/
import Mathlib.RingTheory.KrullDimension.NonZeroDivisors
import Mathlib.RingTheory.Length
import Mathlib.RingTheory.HopkinsLevitzki
/-!
# Order of vani... |
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.
(**************************************************... |
Sections.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Forall2
/-!
# List sections
This file proves some stuff about `List.sections` (definition in `Data.List.Defs`). A section of a
list of lists... |
Cardinality.lean | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
import Mathlib.GroupTheory.MonoidLocalization.Basic
import Mathlib.GroupTheory.OreLocalization.Cardinality
/-!
# Cardinality of localizations of commutative monoids
This file cont... |
ComputeDegree.lean | import Mathlib.Tactic.ComputeDegree
open Polynomial
variable {R : Type*}
section native_mathlib4_tests
variable {n : ℕ} {z : ℤ} {f : ℤ[X]} (hn : natDegree f ≤ 5) (hd : degree f ≤ 5)
/-- Flows through all the matches in `compute_degree`, with a `natDegree _ ≤ _` goal. -/
example : natDegree (- C z * X ^ 5 + (monom... |
Unitor.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.GradedObject.Associator
import Mathlib.CategoryTheory.GradedObject.Single
/-!
# The left and right unitors
Given a bifunctor `F : C ⥤ D ⥤ D`, an ... |
Basic.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fangming Li, Jujian Zhang
-/
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Order.KrullDimension
import Mathlib.RingTheory.Ideal.Quot... |
EventuallyMeasurable.lean | /-
Copyright (c) 2024 Felix Weilacher. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Felix Weilacher
-/
import Mathlib.MeasureTheory.MeasurableSpace.Defs
import Mathlib.Order.Filter.CountableInter
/-!
# Measurability modulo a filter
In this file we consider the gen... |
Modular.lean | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
import Mathlib.LinearAlgebra.Genera... |
Units.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Tactic.Tauto
import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Nat.Units
/-!
# Units in the integers... |
RestrictScalars.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import Mathlib.Algebra.Algebra.Tower
/-!
# The `RestrictScalars` type alias
See the documentation attached to the `RestrictScalars` definition for advice on... |
EulerSineProd.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.Analysis.SpecialFunctions.Integrals.Basic
import Mathlib.MeasureTheory.Integral.PeakFunction
/-! # Euler's infinite product for the sine function
Thi... |
Killing.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Derivation.Killing
import Mathlib.Algebra.Lie.Killing
import Mathlib.Algebra.Lie.Sl2
import Mathlib.Algebra.Lie.Weights.Chain
import Mathlib.Line... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
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, Kevin Buzzard, Kim Morrison, Johan Commelin, Chris Hughes,
Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Hom.Defs... |
Epi.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.Category.Ring.Basic
import Mathlib.RingTheory.TensorProduct.Finite
import Mathlib.CategoryTheory.ConcreteCategory.EpiMono
/-!
# Epimorphisms in `Com... |
Colimits.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Reid Barton, Joël Riou
-/
import Mathlib.Logic.UnivLE
import Mathlib.CategoryTheory.Limits.HasLimits
import Mathlib.CategoryTheory.Limits.Types.ColimitType
/-!
# Colimits ... |
Matrix.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# Finite and free modules using matrices
We provide ... |
Basic.lean | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.SetLike.Basic
import Mathlib.Order.SupIndep
/-!
# Partitions
A `Partition` of an element `a` in a complete lattice is an independent family of nontr... |
CompatiblePlus.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
import Mathlib.CategoryTheory.Sites.Whiskering
import Mathlib.CategoryTheory.Sites.Plus
/-!
In this file, we prove that the plus functor is compatible with functors which
p... |
Defs.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Subse... |
Defs.lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Measure.GiryMonad
/-!
# Markov Kernels
A kernel from a measurable space `α` to another measurable space `β` is a measurable map
`α → Measur... |
Equalizers.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Markus Himmel
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Limits.HasLimits
/-!
# Equalizers and coequalizers
This file defines (co)equalizers a... |
DayConvolution.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.Monoidal.ExternalProduct.KanExtension
import Mathlib.CategoryTheory.Products.Associator
/-!
# Day convolution monoidal structure
Given f... |
Canonical.lean | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Algebra.Order.GroupWithZero.Canonical
import Mathlib.Alg... |
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.
|
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.
|
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 ... |
Sym.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.List.Sym
/-! # Unordered tuples of elements of a multiset
Defines `Multiset.sym` and the specialized `Multiset.sym2` for computing multisets of all
un... |
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... |
Indicator.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.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Indicator
import Mathlib.Order.CompleteLattice.Finset
/-!
# Interaction of big op... |
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... |
Yoneda.lean | /-
Copyright (c) 2021 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.CategoryTheory.Linear.Basic
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# The Yoneda embedd... |
Contrapose.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Tactic.Push
/-! # Contrapose
The `contrapose` tactic transforms the goal into its contrapositive when that goal is an
implication.
* `contrapose` ... |
Dual.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.LinearAlgebra.DFinsupp
import Mathlib.LinearAlgebra.Dual.Basis
import Mathlib.LinearAlgebra.Matrix.ToLin
/-!... |
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... |
Summable.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
import Mathlib.Analysis.PSeries
import Mathlib.Order.Interval.Finset.Box
import Mathlib.Analysis.Asymptotics.... |
PID.lean | /-
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.RingTheory.DedekindDomain.Dvr
import Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas
/-!
# Criteria under which a Dedekind domain is a PID
This file contain... |
NormTrace.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.Norm.Defs
import Mathlib.RingTheory.Trace.Defs
/-!
# Relation between norms and traces
-/
open Module
lemma Algebra.norm_one_add_smul {A B} [Co... |
OrderEmbedding.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Interval.Set.UnorderedInterval
import Mathlib.Order.Hom.Basic
/-!
# Preimages of intervals under order embeddings
In this file we prove that ... |
Notation.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic
import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
/-! # Notations for probability theory
Th... |
Pi.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.Topology.MetricSpace.Pseudo.Pi
import Mathlib.Topology.MetricSpace.Ultra.Basic
/-!
# Ultrametric distances on pi types
This file contains results o... |
TopologicallyNilpotent.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir, María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, María Inés de Frutos-Fernández
-/
import Mathlib.Topology.Algebra.LinearTopology
import Mathlib.RingTheory.Ideal.Basic
imp... |
Grp.lean | import Mathlib.Algebra.Category.Grp.Basic
universe v u
open CategoryTheory Grp
set_option maxHeartbeats 10000
set_option synthInstance.maxHeartbeats 2000
/- We test if all the coercions and `map_add` lemmas trigger correctly. -/
example (X : Type u) [Group X] : ⇑(𝟙 (of X)) = id := by simp
example {X Y : Type u} ... |
Imo2005Q3.lean | /-
Copyright (c) 2021 Manuel Candales. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Manuel Candales
-/
import Mathlib.Data.Real.Basic
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# IMO... |
Defs.lean | /-
Copyright (c) 2022 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Data.Set.CoeSort
import Mathlib.Logic.Equiv.Defs
import Mathlib.Tactic.Set
import Mathlib.Util.AssertExists
/-!
# Definition of the `Finite` typeclass
This... |
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 ... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Equalizer.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.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Subpresheaf.Image
/-!
# The equalizer of two morphisms of presheaves, as a subpresheaf
If... |
Additive.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.Analysis.BoxIntegral.Partition.Split
import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul
/-!
# Box additive functions
We say that a function `f : ... |
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 ... |
IndicatorFunction.lean | /-
Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Yury Kudryashov
-/
import Mathlib.Algebra.Order.Group.Indicator
import Mathlib.Algebra.Order.Pi
import Mathlib.Analysis.Normed.Group.Basic
/-!
# Indicator function and (... |
ShrinkingLemma.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.Topology.EMetricSpace.Paracompact
import Mathlib.Topology.MetricSpace.Basic
import Mathlib.Topology.MetricSpace.ProperSpace.Lemmas
import Mathlib.Top... |
Basic.lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Jujian Zhang
-/
import Mathlib.Algebra.Polynomial.DenomsClearable
import Mathlib.Analysis.Calculus.MeanValue
import Mathlib.Analysis.Calculus.Deriv.Polynomial
import Mathl... |
DefEqTransformations.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Tactic.Basic
/-! # Tactics that transform types into definitionally equal types
This module defines a standard wrapper that can be used to create tactics t... |
Doubling.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.MeasureTheory.Measure.MeasureSpaceDef
/-!
# Uniformly locally doubling measures
A uniformly locally doubl... |
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, Mario Carneiro
-/
import Mathlib.Data.Finset.Update
import Mathlib.Data.Prod.TProd
import Mathlib.Data.Set.UnionLift
import Mathlib.GroupTheory.Coset.Defs
import Mathli... |
action.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype.
From mathcomp Require Import ssrnat div seq prime fintype bigop finset.
From mathcomp... |
Basic.lean | /-
Copyright (c) 2024 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Category.BialgCat.Basic
import Mathlib.RingTheory.HopfAlgebra.Basic
/-!
# The category of Hopf algebras over a commutative ring
We intr... |
Inverse.lean | /-
Copyright (c) 2020 Kenji Nakagawa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenji Nakagawa, Anne Baanen, Filippo A. E. Nuccio
-/
import Mathlib.RingTheory.FractionalIdeal.Operations
/-!
# Inverse operator for fractional ideals
This file defines the notation ... |
Bounded.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, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Continuity
import Mathlib.Topology.MetricSpace.Bounded
import Mathlib.Order.Filter.Pointwise
/-!
#... |
Preserves.lean | /-
Copyright (c) 2025 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Preadditive.Projective.Basic
/-!
# Preservation of projective objects
We define a typeclass `Functor.PreservesProjectiveObjects`.
We re... |
Pi.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.ContinuousFunctionalCalculus.Unique
import Mathlib.Algebra.Algebra.Spectrum.Pi
import Mathlib.Algebra.Star.StarAlgHom
/-! # T... |
Integers.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.RingTheory.Valuation.Basic
/-!
# Ring of integers under a given valuation
The elements with valuation less than or equal to 1.
TODO: Define characteristic pre... |
rewrites.lean | import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.Data.List.InsertIdx
import Mathlib.Algebra.Group.Basic
-- This is partially duplicative with the tests for `rw?` in Lean.
-- It's useful to re-test here with a larger environment.
private axi... |
Basic.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Action.Units
import Mathlib.Algebra.Group.Invertible.Defs
import Mathlib.Algebra.GroupWithZero.U... |
InteriorBoundary.lean | /-
Copyright (c) 2023 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
import Mathlib.Geometry.Manifold.IsManifold.ExtChartAt
/-!
# Interior and boundary of a manifold
Define the interior and boundary of a manifold.
## Main defini... |
LinearIndependent.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.LinearAlgebra.LinearIndependent.Defs
import Mathlib.RingTheory.Algebraic.Defs
/-!
# Linear independence of transcendental elements
## Main result
* ... |
InitTail.lean | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.RingTheory.WittVector.Basic
import Mathlib.RingTheory.WittVector.IsPoly
/-!
# `init` and `tail`
Given a Witt vecto... |
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... |
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... |
hint.lean | import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Tactic.Common
import Mathlib.Tactic.ComputeDegree
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Finiteness
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.TautoSet
/--
info: Try these:
• linarith
-/
#guard_msgs in
example ... |
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 :=... |
Funext.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Polynomial.RingDivision
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.MvPolynomia... |
Support.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Aaron Anderson, Yakov Pechersky
-/
import Mathlib.Data.Fintype.Card
import Mathlib.Algebra.Group.Commute.Basic
import Mathlib.Algebra.Group.End
import Mathlib.Data.Finset.N... |
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... |
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