filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Cat.lean | /-
Copyright (c) 2024 Nicolas Rolland. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rolland
-/
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
/-!
# Chosen finite products in `Cat`
This file proves that the cartesian product of a pair of categories ag... |
Principal.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.RingTheory.SimpleRing.Field
import Mathlib.RingTheory.TwoSidedIdeal.Operations
/-!
# A commutative s... |
OnePointEquiv.lean | /-
Copyright (c) 2024 Bjørn Kjos-Hanssen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bjørn Kjos-Hanssen, Oliver Nash
-/
import Mathlib.Topology.Compactification.OnePoint.ProjectiveLine
deprecated_module (since := "2025-06-04")
|
ring_compare.lean | import Mathlib.Tactic.NormNum.OfScientific
import Mathlib.Tactic.Ring.Compare
import Mathlib.Tactic.Ring.RingNF
open Lean Elab Tactic
elab "ring_le" : tactic => liftMetaFinishingTactic Mathlib.Tactic.Ring.proveLE
elab "ring_lt" : tactic => liftMetaFinishingTactic Mathlib.Tactic.Ring.proveLT
section Nat
variable {x y... |
finfield.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype div tupl... |
Bundled.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johannes Hölzl, Reid Barton, Sean Leather
-/
import Mathlib.Init
import Batteries.Tactic.Lint.Misc
/-!
# Bundled types
`Bundled c` provides a uniform structure for bundli... |
AtPrime.lean | import Mathlib.RingTheory.Localization.AtPrime.Basic
deprecated_module (since := "2025-08-01")
|
Family.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-/
import Mathlib.SetTheory.Cardinal.UnivLE
import Mathlib.SetTheory.Ordinal.Arithmetic
/-!
# Arithmetic on families of or... |
Shrink.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.Logic.Small.Defs
import Mathlib.Topology.Defs.Induced
import Mathlib.Topology.Homeomorph.Defs
/-!
# Topological space structure on `Shrink X`
-/
... |
Functor.lean | /-
Copyright (c) 2017 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import Mathlib.Tactic.Attr.Register
import Mathlib.Data.Set.Defs
import Mathlib.Tactic.TypeStar
import Batteries.Tactic.Lint
/-!
# Functors
This module provides additiona... |
maximal.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import div fintype finfun bigop finset prime binomial.
Fro... |
choice.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(**************************************************... |
commutator.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat fintype.
From mathcomp Require Import bigop finset binomial fingroup morphism.
From mathcomp... |
Basic.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Analysis.Calculus.ContDiff.Defs
import Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno
import Mathlib.Analysis.Calculus.FDeriv.Ad... |
EpiMono.lean | /-
Copyright (c) 2021 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
import Mathlib.CategoryTheory.Limits.Preserves.Shapes... |
ContMDiffMap.lean | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri
-/
import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace
/-!
# `C^n` bundled maps
In this file we define the type `ContMDiffMap` of `n` times continuously differe... |
all_ssreflect.v | Attributes deprecated(since="mathcomp 2.5.0",
note="Use 'all_boot' and/or 'all_order' instead.").
From mathcomp Require Export all_boot.
From mathcomp Require Export preorder.
From mathcomp Require Export order.
|
Star.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Order.Star.Basic
/-!
# Commutative star-ordered rings are ordered rings
A noncommutative star-ordered ri... |
ssrint.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import fintype finfun b... |
Defs.lean | /-
Copyright (c) 2018 Louis Carlin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Louis Carlin, Mario Carneiro
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Order.RelClasses
/-!
# Euclidean domains
This file introduces Euclidean domains and provides the extende... |
Basic.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Ring.Action.Basic
import Mathlib.GroupTheory.Congruence.Basic
import Mathlib.RingTheory.Congruence.Defs
/-!
# Congruence relations on rings
This fi... |
Span.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import Mathlib.Algebra.GroupWithZero.Associated
import Mathlib.Algebra.Ring.Idempotent
import Mathlib.Algebra.Ring.Regular
import Mathlib.LinearAl... |
IsBoundedDefault.lean | import Mathlib.Data.EReal.Basic
import Mathlib.Order.LiminfLimsup
open Filter
variable {α : Type*} {f : Filter α} {u v : α → EReal} (h : u ≤ᶠ[f] v)
-- proof term
example : limsup u f ≤ limsup v f := limsup_le_limsup h
-- exact
example : limsup u f ≤ limsup v f := by exact limsup_le_limsup h
-- apply
example : limsu... |
Affine.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.LinearAlgebra.AffineSpace.AffineMap
import Mathlib.Topology.Algebra.MulAction
import Mathlib.Topology.Algebra.Group.Defs
/-!
# Topological propertie... |
CompTypeclasses.lean | /-
Copyright (c) 2024 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Logic.Function.Defs
/-!
# Propositional typeclasses on several maps
This file contains typeclasses that are used in the definition of
... |
DotProduct.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Data.Matrix.RowCol
import Mathlib.Algebra.Star.Pi
/-!
# Dot product ... |
TypeStar.lean | /-
Copyright (c) 2023 Matthew Robert Ballard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Init
import Lean.Elab.Term
/-!
# Support for `Sort*` and `Type*`.
These elaborate as `Sort u` and `Type u` with a fresh implicit universe variab... |
fingraph.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat.
From mathcomp Require Import seq path fintype.
(******************************************... |
spectral.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp.
From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector.
From mathcomp Require Import mxpoly mxred sesqui... |
fraction.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq.
From mathcomp Require Import ssrAC choice tuple ... |
Order.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
-/
import Mathlib.Data.Set.Basic
/-!
# Order structures and monotonicity lemmas for `Set`
-/
open Function
universe u v
namespace Set
variable {α :... |
Says.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Init
import Lean.Meta.Tactic.TryThis
import Batteries.Linter.UnreachableTactic
import Qq.Match
/-!
# The `says` tactic combinator.
If you write `X says`,... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
Span.lean | /-
Copyright (c) 2024 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.Normed.Operator.LinearIsometry
import Mathlib.Analysis.Normed.Operator.ContinuousLinearMap
import Mathlib.Analysis.Normed.Module.Basic
import Mathl... |
finfield.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype div tupl... |
test_intro_rw.v | From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Lemma test_dup1 : forall n : nat, odd n.
Proof. move=> /[dup] m n; suff: odd n by []. Abort.
Lemma test_dup2 : let n := 1 in False.
Proof. move=> /[dup] m n; have : m = n :=... |
MeasurePreserving.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.MeasureTheory.Integral.Lebesgue.Basic
deprecated_module (since := "2025-04-15")
|
Set.lean | /-
Copyright (c) 2022 Ian Benway. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ian Benway
-/
import Mathlib.Init
import Lean.Elab.Tactic.ElabTerm
/-!
# The `set` tactic
This file defines the `set` tactic and its variant `set!`.
`set a := t with h` is a variant of ... |
CircleTransform.lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Data.Complex.Basic
import Mathlib.MeasureTheory.Integral.CircleIntegral
/-!
# Circle integral transform
In this file we define the circle integral tr... |
Lindelof.lean | /-
Copyright (c) 2023 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
import Mathlib.Topology.Bases
import Mathlib.Order.Filter.CountableInter
import Mathlib.Topology.Compactness.SigmaCompact
/-!
# Lindelöf sets and Lindelöf spaces
## Mai... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Order.SuccPred
import Mathlib.Data.Sum.Order
import Mathlib.SetTheory.Cardinal.Basic
import Mathlib.Tactic.PPWithUniv
/-!
# ... |
Unique.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Function.LocallyIntegrable
import Mathlib.MeasureTheory.Group.Integral
import Mathlib.MeasureTheory.Integral.Prod
import Mathlib.Me... |
MetricSeparated.lean | /-
Copyright (c) 2021 Yury Kudryashov, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Topology.EMetricSpace.Defs
/-!
# Metric separation
This file defines a few notions of separations of sets in a metric s... |
IsSimpleOrder.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.LinearAlgebra.FiniteDimensional.Basic
import Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition
import Mathlib.LinearAlgebra.FreeModule.StrongRankConditi... |
Classification.lean | /-
Copyright (c) 2022 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Algebra.ZMod
import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.MvPolynomial.Cardinal
import Mathlib.FieldTheory.IsAlgClosed.Basic
import Mat... |
Over.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
import Mathlib.CategoryTheory.Limits.Constructions.Over.Products
/-!
# `CartesianMonoidalCategory` for `Over X`
We... |
Basic.lean | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.NeZero
import Mathlib.Data.Nat.Cast.Defs
import Mathlib.Data.Fin.Rev
/-!
# Fin is a group
This file cont... |
seq.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
(******************************************************... |
extraspecial.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype bigop finset prime binomial.
From mathc... |
gfunctor.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype.
From mathcomp Require Import bigop finset fingroup morphism automorphism.
From math... |
Nucleus.lean | /-
Copyright (c) 2024 Christian Krause. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chriara Cimino, Christian Krause
-/
import Mathlib.Order.Closure
import Mathlib.Order.Hom.CompleteLattice
/-!
# Nucleus
Locales are the dual concept to frames. Locale theory is a b... |
Image.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Set.Lattice
import Mathlib.Tactic.Monotonicity.Attr
/-!
# The set lattice and (pre)images of fun... |
all_ssreflect.v | Attributes deprecated(since="mathcomp 2.5.0",
note="Use 'all_boot' and/or 'all_order' instead.").
From mathcomp Require Export all_boot.
From mathcomp Require Export preorder.
From mathcomp Require Export order.
|
FiniteDimensionalLaws.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Jonas Bayer
-/
import Mathlib.MeasureTheory.Constructions.Projective
import Mathlib.Probability.IdentDistrib
/-!
# Finite dimensional distributions of a stochastic proces... |
ENNReal.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
import Mathlib.MeasureTheory.Integral.Lebesgue.Add
/-!
# Finitely strongly measurable func... |
polyXY.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype tuple fi... |
WithDensity.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.MeasureTheory.Integral.Lebesgue.Countable
import Mathlib.MeasureTheory.Measure.Decomposition.Exhaustion
import Mathlib.MeasureTheory.Gr... |
Lattice.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.Group.Action.Defs
import Mathlib.Data.Nat.Lattice
import Mathlib.Data.ENat.Basic
/-!
# Extended natural numbers form a complete linear order... |
Prefunctor.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn, Kim Morrison
-/
import Mathlib.Combinatorics.Quiver.Basic
/-!
# Morphisms of quivers
-/
universe v₁ v₂ u u₁ u₂
/-- A morphism of quivers. As we will later have categorical f... |
Basic.lean | /-
Copyright (c) 2020 Gihan Marasingha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gihan Marasingha
-/
import Mathlib.Tactic.Linarith
/-!
# An MIU Decision Procedure in Lean
The [MIU formal system](https://en.wikipedia.org/wiki/MU_puzzle) was introduced by Dougla... |
NormedSpace.lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
import Mathlib.Analysis.Normed.Module.Span
import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear
import Mathlib.Analysis.NormedS... |
path.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(******************************************************************************)
(* ... |
polyXY.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype tuple fi... |
AlexDisc.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Topology.Specialization
/-!
# Category of Alexandrov-discrete topological spaces
This defines `AlexDisc`, the category of Alexandrov-discrete topological... |
NoetherNormalization.lean | /-
Copyright (c) 2025 Sihan Su. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Sihan Su, Wan Lin, Xiaoyang Su
-/
import Mathlib.Algebra.MvPolynomial.Monad
import Mathlib.Data.List.Indexes
import Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basi... |
MeasurableLIntegral.lean | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.MeasurableSpace.Prod
import Mathlib.Probability.Kernel.Basic
/-!
# Measurability of the integral against a kernel
The Lebesgue integral of ... |
Finset.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Data.Finset.Density
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Tactic.Positivity.Core
/-!
#... |
Rify.lean | import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Rify
set_option linter.unusedVariables false
example {n : ℕ} {k : ℤ} (hn : 8 ≤ n) (hk : 2 * k ≤ n + 2) :
(0 : ℝ) < n - k - 1 := by
rify at hn hk
linarith
example {n : ℕ} {k : ℤ} (hn : 8 ≤ n) (hk : (2 : ℚ) * k ≤ n + 2) :
(0 : ℝ) < n - k - 1 := by
rify... |
EraseLead.lean | /-
Copyright (c) 2020 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Alex Meiburg
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.Polynomial.Degree.Lemmas
import Mathlib.Algebra.Polynomial.Degree.Monomial
/-!
# Erase the... |
Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Data.Fin.VecNotation
import Mathlib.Logic.Embedding.Set
import Mathlib.Logic.Equiv.Option
import Mathlib.Data.Int.Init
/-!
# Equivalences for `Fin n`
-/
assert... |
OneVariable.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
/-! # Jacobi's theta function
This fil... |
Constructions.lean | /-
Copyright (c) 2023 Geoffrey Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Geoffrey Irving, Stefan Kebekus
-/
import Mathlib.Analysis.Analytic.Composition
import Mathlib.Analysis.Analytic.Linear
import Mathlib.Analysis.NormedSpace.OperatorNor... |
burnside_app.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
Multiset.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Order.Group.Finset
import Mathlib.Data.Finsupp.Basic
import Mathlib.Data.Sym.Basic
import Mathlib.Order.Preorder.Finsupp
/-!
# Equivalence bet... |
closed_field.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype generic_... |
interval_inference.v | (* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice.
From mathcomp Require Import order ssralg ssrnum ssrint interval.
(**md********************************************************... |
inertia.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div... |
Defs.lean | /-
Copyright (c) 2017 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johannes Hölzl, Chris Hughes, Jens Wagemaker, Jon Eugster
-/
import Mathlib.Algebra.Group.Commute.Defs
/-!
# Units (i.e., invertible elements) of a monoid
An el... |
bigop.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
WeakOperatorTopology.lean | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.LocallyConvex.WeakOperatorTopology
/-!
# The weak operator topology in Hilbert spaces
This... |
LocalClosure.lean | /-
Copyright (c) 2025 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.Basic
/-!
# Local closure of morphism properties
We define the source local closure of a property `P` wrt. a morphism... |
Pullbacks.lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Andrew Yang
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
import Mathlib.CategoryTheory.Limits.Preserves.Basic
import Mathlib.CategoryTheory.Limits.Op... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Control.Combinators
import Mathlib.Logic.Function.Defs
import Mathlib.Tactic.CasesM
import Mathlib.Tactic.Attr.Core
/-!
Extends the theory on functors... |
closed_field.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import fintype generic_... |
test_regular_conv.v | From mathcomp Require Import all_boot all_order all_algebra all_field.
Section regular.
Import GRing.
Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType.
Proof. by move=> [? []]. Qed.
Goal forall R : comRingType, [the algType R of R^o] = R :> ringType.
Proof. by move=> [? []]. Qed.
Goal forall R : c... |
algebraics_fundamentals.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice.
From mathcomp Require Import div fintype path... |
Variable.lean | import Mathlib.Algebra.Algebra.Defs
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Ring.Regular
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.RingTheory.UniqueFactorizationDomain.Basic
import Mathlib.Tactic.Variable
set_option autoImplicit true
namespace Tests... |
Operations.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Johannes Hölzl, Reid Barton, Kim Morrison, Patrick Massot, Kyle Miller,
Minchao Wu, Yury Kudryashov, Floris van Doorn
-/
import Mathlib.Data.Set.CoeSort
import Mathlib.Da... |
numdomain.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import ssrAC div fintyp... |
ReImTopology.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle
/-!
# Closure, interior, and frontier of preimages under `re`... |
ring_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq ssralg generic_q... |
ValuativeRel.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.RingTheory.Valuation.ValuativeRel
import Mathlib.Topology.Algebra.Valued.ValuationTopology
import Mathlib.Topology.Algebra.WithZeroTopology
/-!
# V... |
ring_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq ssralg generic_q... |
TransferInstance.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Data.Fintype.Basic
/-!
# Transfer algebraic structures across `Equiv`s
I... |
Defs.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.RingTheory.SimpleRing.Basic
/-!
# Finite dimensional vector spa... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
Lemmas.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Joey van Langen, Casper Putz
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Data.Nat.Multiplicity
import Mathlib.Data.Nat.Choose.Sum
/-!
# Characteristic of semirings
-/
a... |
Hom.lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Chris Hughes, Kevin Buzzard
-/
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.Algebra.Group.Hom.Basic
import Mathlib.Algebra.Group.Units.Basic
/-!
# Monoid hom... |
Positivity.lean | import Mathlib.Tactic.Positivity.Basic
import Mathlib.Tactic.Positivity.Finset
import Mathlib.Tactic.NormNum.Basic
import Mathlib.Data.Int.Order.Basic
|
poly.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop fi... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.