filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
RadonNikodym.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
/-!
# Radon-Nikodym theorem
Th... |
Field.lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Order.Field.Canonical
import Mathlib.Algebra.Order.Nonneg.Ring
import Mathlib.Data.Nat.Cast.Order.Ring
... |
Map.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.MeasureTheory.Integral.Lebesgue.Add
/-!
# Behavior of the Lebesgue integral under ma... |
Point.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.AlgebraicGeometry.EllipticCurve.Affine.Formula
import Mathlib.LinearAlgebra.FreeModule.Norm
import Mathlib.RingTheory.ClassGroup
im... |
AddRelatedDecl.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Floris van Doorn
-/
import Mathlib.Init
import Lean.Elab.DeclarationRange
import Lean.Elab.Term
/-!
# `addRelatedDecl`
-/
open Lean Meta Elab
namespace Mathlib.Tactic
... |
nmodule.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun monoid.
(******************************************************************************)
(* Additive group-like structures ... |
GlobalAttributeIn.lean | /-
Copyright (c) 2024 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang, Damiano Testa
-/
import Lean.Elab.Command
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and module docstring.
import Ma... |
borelize.lean | import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
set_option autoImplicit true
example [TopologicalSpace α] [inst : MeasurableSpace α] [BorelSpace α] :
MeasurableSet (∅ : Set α) := by
guard_target = @MeasurableSet α inst ∅
borelize α
guard_target = @MeasurableSet α (borel α) ∅
apply MeasurableSe... |
InvariantForm.lean | /-
Copyright (c) 2024 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Lie.Semisimple.Defs
import Mathlib.LinearAlgebra.BilinearForm.Orthogonal
/-!
# Lie algebras with non-degenerate invariant bilinear forms are s... |
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, Yury Kudryashov
-/
import Mathlib.Data.Set.SymmDiff
import Mathlib.Order.SuccPred.Relation
import Mathlib.Topology.Irreducible
/-!
# Connected subsets ... |
Star.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.Analysis.Calculus.FDeriv.Linear
import Mathlib.Analysis.Calculus.FDeriv.Comp
import Mathlib.Analysis.Calculus.FDeriv.Equiv
import Mathlib.Analysis.CStarAlgeb... |
vector.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop fi... |
Get.lean | /-
Copyright (c) 2019 mathlib community. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Wojciech Nawrocki
-/
import Mathlib.Data.Num.Basic
import Mathlib.Data.Ordering.Basic
import Mathlib.Data.Tree.Basic
/-!
# Binary tree get operation
In this file w... |
LocalizationAway.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.RingTheory.Extension.Presentation.Basic
/-!
# Cotangent and localization away
Let `R → S → T` be algebras such that `T` is the localization of `S... |
Defs.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Data.Set.Operations
import Mathlib.Logic.Function.Iterate
import Mathlib.Order.Basic
import Mathlib.Tactic.Coe
import Mathl... |
zmodp.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 choice eqtype ssrnat seq.
From mathcomp Require Import div fintype bigo... |
Small.lean | /-
Copyright (c) 2025 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, Maria-Inés de Frutos-Fernandez
-/
import Mathlib.LinearAlgebra.Finsupp.LinearCombination
import Mathlib.RingTheory.FiniteT... |
NoncommPiCoprod.lean | /-
Copyright (c) 2022 Joachim Breitner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
import Mathlib.GroupTheory.OrderOfElement
import Mathlib.Data.Nat.GCD.BigOperators
import Mathlib.Order.SupIndep
/-!
# Canonical homomorphism from a finite famil... |
Lattice.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.Data.Fintype.Lattice
import Mathlib.RingTheory.Finiteness.Basic
/-!
# Finite suprema of finite modules
-/
namespace Submodule
open Module
variable... |
FloorPow.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.Algebra.Order.Field.GeomSum
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Results on disc... |
Trim.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.Measure.Typeclasses.SFinite
/-!
# Restriction of a measure to a sub-σ-algebra
## Main definitions
* `MeasureTheory.Measure.trim`: restric... |
Semiconj.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Yury Kudryashov, Neil Strickland
-/
import Mathlib.Algebra.Group.Semiconj.Defs
import Mathlib.Algebra.Ring.Defs
/-!
# Semirings and ... |
Minimal.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Peter Nelson
-/
import Mathlib.Order.Antichain
/-!
# Minimality and Maximality
This file proves basic facts about minimality and maximality
of an element with respect to ... |
Choose.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Mario Carneiro, Reid Barton, Johan Commelin
-/
import Mathlib.Util.Tactic
import Mathlib.Logic.Function.Basic
/-!
# `choose` tactic
Performs Skolemi... |
Whiskering.lean | import Mathlib.Algebra.Category.ModuleCat.Colimits
import Mathlib.Algebra.Category.ModuleCat.Limits
import Mathlib.Algebra.Category.ModuleCat.FilteredColimits
import Mathlib.CategoryTheory.Sites.Equivalence
universe u
open CategoryTheory GrothendieckTopology
section Small
variable {C : Type u} [SmallCategory C] (J ... |
Unitization.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.Analysis.CStarAlgebra.Classes
import Mathlib.Analysis.Normed.Algebra.Unitization
/-! # The minimal unitization of a C⋆-algebra
This file shows that when... |
Sober.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Topology.Sets.Closeds
import Mathlib.Topology.Sets.OpenCover
/-!
# Sober spaces
A quasi-sober space is a topological space where every irreducible closed s... |
Ring.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, Andrew Yang
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Math... |
Star.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.Order.Monoid.Submonoid
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Algebra.Order.Ring.Int
import ... |
WithLp.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Eric Wieser
-/
import Mathlib.Analysis.Calculus.ContDiff.Operations
import Mathlib.Analysis.Normed.Lp.PiLp
/-!
# Derivatives on `WithLp`
-/
section PiLp
open Con... |
Presheaf.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit
import Mathlib.CategoryTheory.Limits.Elements
/-!
# Finite-limit-preserving presheaves
In this... |
Basic.lean | /-
Copyright (c) 2024 Floris van Doorn and Hannah Scholz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Hannah Scholz
-/
import Mathlib.Analysis.NormedSpace.Real
import Mathlib.Data.ENat.Basic
import Mathlib.Logic.Equiv.PartialEquiv
import Mathlib.T... |
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.Algebra.Category.ModuleCat.Differentials.Basic
/-!
# The presheaf of differentials of a presheaf of modules
... |
Cotangent.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.Algebra.Module.Torsion
import Mathlib.Algebra.Ring.Idempotent
import Mathlib.LinearAlgebra.Dimension.Finite
import Mathlib.LinearAlgebra.Dimension.FreeAndStr... |
NatAntidiagonal.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.Algebra.Order.Antidiag.Prod
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Data.Multiset.NatAntidiagonal
/-!
# Antidiagonals in ℕ × ℕ as finset... |
Indicator.lean | /-
Copyright (c) 2020 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Sébastien Gouëzel
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
import Mathlib.MeasureTheory.Function.LpSpace.Basic
import Mathlib.MeasureTheory.Measure.Real
i... |
Kernels.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.Algebra.Category.ModuleCat.EpiMono
import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
/-!
# The concrete (co)kernels in the category of modules ... |
OfScalars.lean | /-
Copyright (c) 2024 Edward Watine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward Watine
-/
import Mathlib.Analysis.Analytic.ConvergenceRadius
/-!
# Scalar series
This file contains API for analytic functions `∑ cᵢ • xⁱ` defined in terms of scalars
`c₀, c₁, ... |
HeytAlg.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Category.BddDistLat
import Mathlib.Order.Heyting.Hom
/-!
# The category of Heyting algebras
This file defines `HeytAlg`, the category of Heyting al... |
VectorSpace.lean | /-
Copyright (c) 2022 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Group.UniqueProds.Basic
import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
# A `ℚ`-vector space has `TwoUniqueSums`.
-/
variable {G : Type*}
/... |
Dyadic.lean | /-
Copyright (c) 2021 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.Order.Group.Basic
import Mathlib.Algebra.Ring.Regular
import Mathlib.GroupTheory.MonoidLocalization.Away
impo... |
IntermediateField.lean | /-
Copyright (c) 2024 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
import Mathlib.FieldTheory.IntermediateField.Adjoin.Defs
import Mathlib.Topology.Algebra.Field
/-!
# Continuous actions related to intermediate fields
In this file we... |
Interval.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Data.Finset.Finsupp
import Mathlib.Data.Finsupp.Order
import Mathlib.Order.Interval.Finset.Basic
/-!
# Finite intervals of finitely supported functions
T... |
Localization.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.RingTheory.Ideal.MinimalPrime.Basic
import Mathlib.RingTheory.Localization.AtPrime.Basic
/-!
# Minimal primes and localization
We provide various results ... |
RingDivision.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker, Johan Commelin
-/
import Mathlib.Algebra.Polynomial.AlgebraMap
import Mathlib.Algebra.Polynomial.Div
import Mathlib.RingTheory... |
Basic.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Jujian Zhang, Yongle Hu
-/
import Mathlib.Algebra.Colimit.TensorProduct
import Mathlib.Algebra.DirectSum.Finsupp
import Mathlib.Algebra.DirectSum.Module
import Mathlib.... |
Classes.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Algebra.Star.NonUnitalSubalgebra
/-! # Classes of C⋆-algebras
This file defines classes for complex C⋆-algebras.... |
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, Chris Hughes, Mario Carneiro
-/
import Mathlib.RingTheory.LocalRing.Defs
import Mathlib.RingTheory.Ideal.Nonunits
/-!
# Local rings
We prove basic properties of local rings.
... |
DMatrix.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.Group.Hom.Defs
import Mathlib.Algebra.Group.Pi.Basic
/-!
# Dependent-typed matrices
-/
universe u u' v w z
/-- `DMatrix m n` is the type of dep... |
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... |
BaireMeasurable.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.Topology.LocallyClosed
import Mathlib.MeasureTheory.MeasurableSpace.EventuallyMeasurable
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
... |
Real.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Order
import Mathlib.MeasureTheory.MeasurableSpace.Prod
import Mathlib.MeasureTheory.Measure.Ty... |
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.Subgroup
import Mathlib.Algebra.Ring.Subring.Basic
import Mathlib.Algebra.Ring.Subsemiring.Pointwise
/-! # Pointwise instances on `Sub... |
Card.lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Kim Morrison
-/
import Mathlib.GroupTheory.Coset.Basic
import Mathlib.SetTheory.Cardinal.Finite
/-!
# Lagrange's theorem: the order of a subgroup divides the order o... |
NormalForms.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.Tactic.Zify
import Mathlib.Data.List.Sort
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum.Ineq
import Mathlib.Tactic.Ring.Basic
/-! # Norma... |
Range.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, Kyle Miller
-/
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.ULift
/-!
# Finiteness of `Set.range`
## Implementation notes
Each result in ... |
Basic.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.Algebra.Group.Torsion
import Mathlib.Algebra.Notation.Pi.Basic
import Mathlib.Data.FunLike.Basic
import Mathlib.Logic.Function.Iterate
import Mathlib.L... |
Distinguished.lean | /-
Copyright (c) 2024 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
import Mathlib.RingTheory.Polynomial.Eisenstein.Basic
import Mathlib.RingTheory.PowerSeries.Order
/-!
# Distinguished polynomial
In this file we define the predicate `Po... |
LocallySmall.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.Preserves.Ulift
import Mathlib.CategoryTheory.Limits.IndYoneda
import Mathlib.CategoryTheory.Limits.Indization.IndObject
/-!
# The... |
Embedding.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.MeasureTheory.MeasurableSpace.Constructions
import Mathlib.Tactic.FunProp
/-!
# Measurable embeddings and equivalences
A measurable e... |
DirectLimit.lean | /-
Copyright (c) 2023 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.Algebra.Colimit.Module
import Mathlib.LinearAlgebra.TensorProduct.Basic
/-!
# Tensor product and direct limits commute with each other.
Given a family o... |
Basic.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique
import Mathlib.Topology.ContinuousMap.ContinuousSqrt
import Mathlib.Topology.ContinuousMap.Sto... |
finfun.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple.
... |
Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.ContDiff.Operations
import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# Infinitely smooth "bump" func... |
vcharacter.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype... |
CofilteredLimit.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.Topology.Category.Profinite.Basic
import Mathlib.Topology.LocallyConstant.Basic
import Mathlib.Topology.DiscreteQuotient
import Mathlib.Topology.Category.TopCa... |
Cofinal.lean | /-
Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernández Palacios
-/
import Mathlib.Order.GaloisConnection.Basic
import Mathlib.Order.Interval.Set.Basic
import Mathlib.Order.WellFounded
/-!
# Cofinal sets
A se... |
Sign.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Eric Wieser
-/
import Mathlib.Data.Real.Basic
import Mathlib.Tactic.NormNum.Inv
/-!
# Real sign function
This file introduces and contains some results about `Real.sign` wh... |
monoid.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun.
(******************************************************************************)
(* Group-like structures ... |
Datatypes.lean | /-
Copyright (c) 2024 Vasily Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasily Nesterov
-/
import Mathlib.Init
import Batteries.Data.Rat.Basic
import Std.Data.HashMap.Basic
/-!
# Datatypes for the Simplex Algorithm implementation
-/
namespace Mathlib.Ta... |
finset.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat div seq.
From mathcomp Require Import choice fintype finf... |
RingHom.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston, Jireh Loreaux
-/
import Mathlib.Algebra.Divisibility.Hom
import Mathlib.Algebra.Ring.Hom.Defs
import Mathlib.Data.Set.Insert
/-!
# Additional lemmas about homomo... |
DeriveToExpr.lean | import Lean
namespace DeriveToExprTests
open Lean
-- set_option trace.Elab.Deriving.toExpr true
inductive MyMaybe (α : Type u)
| none | some (x : α)
deriving ToExpr
run_cmd Elab.Command.liftTermElabM do
guard <| "MyMaybe.some 2" == s!"{← Lean.PrettyPrinter.ppExpr <| toExpr (MyMaybe.some 2)}"
run_cmd Elab.Com... |
finfield.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype div tupl... |
MvPolynomial.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.LinearAlgebra.DirectSum.Finsupp
import Mathlib.Algebra.MvPolynomial.Eval
import Mathlib.RingTheory.TensorProduct.Basic
import Mathlib.Al... |
Indization.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.Abelian.GrothendieckAxioms.FunctorCategory
import Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Types
import Mathlib.CategoryTheory.Ab... |
preorder.v | (* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import path fintype tup... |
Basic.lean | /-
Copyright (c) 2020 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Algebra.Algebra.Spectrum.Basic
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
import Mathl... |
Roth.lean | /-
Copyright (c) 2022 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Combinatorics.Additive.AP.Three.Defs
import Mathlib.Combinatorics.Additive.Corner.Defs
import Mathlib.Combinatorics.SimpleGraph... |
Reflection.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.Fin.VecNotation
import Mathlib.Algebra.BigOperators.Fin
/-!
# Lemmas for tuples `Fin m → α`
This file contains alternative definitions of common opera... |
AdjointAction.lean | /-
Copyright (c) 2024 Frédéric Marbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Marbach
-/
import Mathlib.Algebra.Lie.Abelian
import Mathlib.Algebra.Lie.Derivation.Basic
import Mathlib.Algebra.Lie.OfAssociative
/-!
# Adjoint action of a Lie algebra on ... |
Productive.lean | /-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.WSeq.Relation
/-!
# Productive weak sequences
This file defines the property of a weak sequence being productive as never stalling – the ... |
Connect.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.Algebra.Homology.Embedding.RestrictionHomology
/-!
# Connecting a chain complex and a cochain complex
Given a chain complex `K`: `... ⟶ K.X 2 ⟶ K.X 1 ⟶ K.X 0`,... |
Multivariate.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Simon Hudon
-/
import Mathlib.Data.Fin.Fin2
import Mathlib.Data.TypeVec
import Mathlib.Logic.Equiv.Defs
/-!
# Functors between the category of tuples of... |
orderedzmod.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import ssrAC div fintyp... |
LocalizerMorphism.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Localization.Equivalence
/-!
# Morphisms of localizers
A morphism of localizers consists of a functor `F : C₁ ⥤ C₂` between
two categories equip... |
finset.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat div seq.
From mathcomp Require Import choice fintype finf... |
mxred.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype finfun bigop fingroup perm order.
From ... |
zmodp.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 choice eqtype ssrnat seq.
From mathcomp Require Import div fintype bigo... |
Op.lean | /-
Copyright (c) 2025 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Opposites
/-!
# The dualizing functor on `Cat`
We define a (strict) functor `opFunctor`... |
InjectiveSeminorm.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.Analysis.NormedSpace.PiTensorProduct.ProjectiveSeminorm
import Mathlib.LinearAlgebra.Isomorphisms
/-!
# Injective seminorm on the tensor of a finite famil... |
test_guard.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Inductive tree := Node { children : seq tree }.
Inductive ptree (T : Type) := singleton of T | branch of list (ptree T).
(* has *)
Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :... |
Exactness.lean | /-
Copyright (c) 2024 Sihan Su. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sihan Su, Yongle Hu, Yi Song
-/
import Mathlib.Algebra.Exact
import Mathlib.RingTheory.LocalProperties.Submodule
import Mathlib.RingTheory.Localization.Away.Basic
import Mathlib.Algebra.Modu... |
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.
(********************************************************************... |
Preorder.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stephen Morgan, Kim Morrison, Johannes Hölzl, Reid Barton
-/
import Mathlib.CategoryTheory.Equivalence
import Mathlib.CategoryTheory.EqToHom
import Mathlib.Order.Hom.Basic
import Mathlib... |
ssrnat.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Import PosDef.
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype.
#[export] Set Warnings "-ov... |
Bifunctor.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Localization.Prod
import Mathlib.CategoryTheory.Functor.Currying
/-!
# Lifting of bifunctors
In this file, in the context of the localization of... |
peel.lean | import Mathlib.Tactic.Peel
import Mathlib.Topology.Instances.Real.Lemmas
open Filter Topology
/-! ## General usage -/
example (p q : Nat → Prop) (h₁ : ∀ x, p x) (h₂ : ∀ x, p x → q x) : ∀ y, q y := by
peel 1 h₁
rename_i y
guard_target =ₐ q y
exact h₂ _ this
example (p q : Nat → Prop) (h₁ : ∀ {x}, p x) (h₂ : ... |
MulEquivHaarChar.lean | /-
Copyright (c) 2025 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.MeasureTheory.Measure.Haar.Unique
/-!
# Scaling Haar measure by a continuous isomorphism
If `G` is a locally compact topological group and `μ` is a reg... |
Commute.lean | /-
Copyright (c) 2014 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Commute
import Mathlib.Algebra.Ring.Commute
/-!
# Cast of natural numbers: lemmas about `Commute`
-/
variable {α : Type*}
nam... |
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