filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Traj.lean | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent
import Mathlib.MeasureTheory.Function.FactorsThrough
import Mathlib.MeasureTheory.Measure.Probabili... |
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... |
FourierTransformDeriv.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, David Loeffler, Heather Macbeth, Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.Analysis.Calculus.ContDiff.CPolynomial
import... |
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, Jens Wagemaker, Aaron Anderson
-/
import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
import Mathlib.Algebra.Group.Submonoid.BigOperators
import Mathlib.Algebra.Gr... |
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.
(********************************************************************... |
Complex.lean | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.MeasureTheory.VectorMeasure.Basic
import Mathlib.Analysis.Complex.Basic
/-!
# Complex measure
This file defines a complex measure to be a vector measure wi... |
Simp.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Gabriel Ebner, Floris van Doorn
-/
import Mathlib.Init
import Lean.Elab.Tactic.Simp
/-!
# Helper functions for using the simplifier.
[TODO] Needs documentation, cleanup, ... |
Rank.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.Algebra.MvPolynomial.Cardinal
import Mathlib.RingTheory.Algebraic.LinearIndependent
import Mathlib.RingTheory.Algebraic.MvPolynomial
import Mathlib.RingTheory.Localiza... |
Symm.lean | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Init
import Lean.Meta.Tactic.Symm
/-!
# `relSidesIfSymm?`
-/
open Lean Meta Symm
namespace Mathlib.Tactic
open Lean.Elab.Tactic
/-- If `e` is the form... |
ExistsI.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Gabriel Ebner, Moritz Doll
-/
import Mathlib.Init
/-!
# The `existsi` tactic
This file defines the `existsi` tactic: its purpose is to instantiate existential quantifiers... |
Generators.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.Sheaf.Free
import Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous
import Mathlib.CategoryTheory.Sites.CoversTop
/-!
#... |
DiscreteSubset.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Bhavik Mehta, Daniel Weber, Stefan Kebekus
-/
import Mathlib.Tactic.TautoSet
import Mathlib.Topology.Constructions
import Mathlib.Data.Set.Subset
import Mathlib.Topology.Sepa... |
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... |
Basic.lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Zhangir Azerbayev
-/
import Mathlib.GroupTheory.Perm.Sign
import Mathlib.LinearAlgebra.LinearIndependent.Defs
import Mathlib.LinearAlgebra.Multilinear.Basis
/-!
# Alte... |
tuple.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.
From mathcomp Require Import seq choice fintype path.
S... |
IsSMulRegular.lean | /-
Copyright (c) 2024 Brendan Murphy. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Brendan Murphy
-/
import Mathlib.Algebra.Module.Torsion
import Mathlib.RingTheory.Flat.Basic
import Mathlib.RingTheory.Ideal.AssociatedPrime.Basic
import Mathlib.RingTheory.QuotSMulTop... |
sylow.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import fintype prime bigop finset fingroup morphism.
From mat... |
Pi.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot
-/
import Mathlib.Algebra.GroupWithZero.Action.Pi
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Regular.SMul
import Mathlib.Algebra.Ring.Pi
/-!
# ... |
order.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... |
Radical.lean | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.LinearAlgebra.Quotient.Basic
import Mathlib.RingTheory.Finiteness.Basic
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Ideal.Quotient.Defs
/-!
#... |
Parametrized.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.Adjunction.Basic
/-!
# Adjunctions with a parameter
Given bifunctors `F : C₁ ⥤ C₂ ⥤ C₃` and `G : C₁ᵒᵖ ⥤ C₃ ⥤ C₂`,
this file introduces the notat... |
LDL.lean | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
import Mathlib.LinearAlgebra.Matrix.PosDef
/-! # LDL decomposition
This file proves the LDL-decom... |
Basic.lean | /-
Copyright (c) 2024 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen, Mitchell Lee, Óscar Álvarez
-/
import Mathlib.Algebra.Group.Subgroup.Pointwise
import Mathlib.Algebra.Ring.Int.Parity
import Mathlib.GroupTheory.Coxeter.Matrix
import Mat... |
Dirac.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.MeasureTheory.MeasurableSpace.CountablyGenerated
import Mathlib.MeasureTheory.Measure.MutuallySingular
import Mathlib.MeasureTheory.Measure.Typeclasses... |
Use.lean | /-
Copyright (c) 2022 Arthur Paulino. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino
-/
import Mathlib.Tactic.Use
import Mathlib.Tactic.Basic
namespace UseTests
set_option autoImplicit true
example : ∃ x : Nat, x = x := by use 42
-- Since `Eq` is an... |
MorphismProperty.lean | /-
Copyright (c) 2024 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.PathCategory.Basic
import Mathlib.CategoryTheory.MorphismProperty.Composition
/-!
# Properties of morphisms in a path category.
We provi... |
FractionalIdeal.lean | /-
Copyright (c) 2024 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.NumberTheory.NumberField.Basic
import Mathlib.RingTheory.FractionalIdeal.Norm
import Mathlib.RingTheory.FractionalIdeal.Operations
/-!
# Fractional ide... |
Bounded.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.Analysis.LocallyConvex.Bounded
import Mathlib.Topology.Algebra.Module.Multilinear.Basic
/-!
# Images of (von Neumann) bounded sets under continuous ... |
algebra_rat.lean | import Mathlib.Algebra.Algebra.Rat
/-- The two `Algebra ℚ≥0 ℚ≥0` instances should coincide. -/
example : DivisionSemiring.toNNRatAlgebra = Algebra.id ℚ≥0 := rfl
/-- The two `Algebra ℚ ℚ` instances should coincide. -/
example : DivisionRing.toRatAlgebra = Algebra.id ℚ := rfl
|
Oplax.lean | /-
Copyright (c) 2024 Calle Sönne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno, Calle Sönne
-/
import Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax
/-!
# Modifications between oplax transformations
A modification `Γ` between oplax tran... |
Basic.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import Mathlib.Control.Functor.Multivariate
import Mathlib.Data.PFunctor.Univariate.Basic
/-!
# Multivariate polynomial functors.
Multivariate polynomial... |
Quaternion.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.GroupTheory.SpecificGroups.Dihedral
/-!
# Quaternion Groups
We define the (generalised) quat... |
algC.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... |
ClassEquation.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Rodriguez
-/
import Mathlib.Algebra.BigOperators.Finprod
import Mathlib.Algebra.Group.ConjFinite
import Mathlib.Algebra.Group.Subgroup.Finite
import Mathlib.Data.... |
Lex.lean | /-
Copyright (c) 2025 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.Order.Monoid.Defs
import Mathlib.Order.PiLex
import Mathlib.RingTheory.HahnSeries.Addition
/-!
# Lexicographic... |
Imo1981Q3.lean | /-
Copyright (c) 2020 Kevin Lacker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Lacker
-/
import Mathlib.Data.Int.Lemmas
import Mathlib.Data.Nat.Fib.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
/-!
# IMO 1981 Q3
Determine the ... |
Limits.lean | /-
Copyright (c) 2023 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz, Dagur Asgeirsson
-/
import Mathlib.Topology.Category.CompHaus.Basic
import Mathlib.Topology.Category.CompHausLike.Limits
/-!
# Explicit limits and colimits
This file applies ... |
Expect.lean | /-
Copyright (c) 2024 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.Algebra.Algebra.Rat
import Mathlib.Algebra.BigOperators.GroupWithZero.Action
import Mathlib.Algebra.BigOperators.Pi
import Math... |
CoverLifting.lean | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Joël Riou
-/
import Mathlib.CategoryTheory.Adjunction.Restrict
import Mathlib.CategoryTheory.Functor.KanExtension.Adjunction
import Mathlib.CategoryTheory.Sites.Continuous
im... |
frobenius.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 div.
From mathcomp Require Import fintype bigop prime finset fingroup morphism.
From mathcom... |
Lucas.lean | /-
Copyright (c) 2023 Gareth Ma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gareth Ma
-/
import Mathlib.Algebra.CharP.Lemmas
import Mathlib.Data.ZMod.Basic
import Mathlib.RingTheory.Polynomial.Basic
/-!
# Lucas's theorem
This file contains a proof of [Lucas's the... |
Cone.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Artie Khovanov
-/
import Mathlib.Algebra.Order.Group.Cone
import Mathlib.Algebra.Ring.Subsemiring.Order
/-!
# Construct ordered rings ... |
AsPolynomial.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, María Inés de Frutos-Fernández, Filippo A. E. Nuccio
-/
import Mathlib.FieldTheory.RatFunc.Basic
import Mathlib.RingTheory.EuclideanDomain
import Mathlib.RingTheory.DedekindD... |
Inv.lean | /-
Copyright (c) 2019 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.Data.ENNReal.Inv
import Mathlib.Data.EReal.Operations
import Mathlib.Data.Sign.Basic
import Mathlib.Data.Nat.Cast.Order.Field
/-!
# Absolute value, sign... |
SingleFunctors.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.Shift.CommShift
/-!
# Functors from a category to a category with a shift
Given a category `C`, and a category `D` equipped with a shift by a mo... |
Real.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying, Eric Wieser
-/
import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv
import Mathlib.Data.Sign.Basic
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Ana... |
Integration.lean | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich, Vincent Beffara
-/
import Mathlib.Probability.Independence.Integration
deprecated_module (since := "2025-07-30")
|
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... |
Basic.lean | /-
Copyright (c) 2024 Yuma Mizuno. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuma Mizuno
-/
import Mathlib.Tactic.CategoryTheory.Coherence.Basic
import Mathlib.Tactic.CategoryTheory.Monoidal.Normalize
import Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence
/-... |
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... |
countalg.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 ss... |
GoldenRatio.lean | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu, Kamila Szewczyk
-/
import Mathlib.Algebra.EuclideanDomain.Basic
import Mathlib.Algebra.LinearRecurrence
import Mathlib.Data.Fin.VecNotati... |
Tree.lean | /-
Copyright (c) 2024 Daniel Weber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Weber
-/
import Mathlib.Order.SuccPred.Archimedean
import Mathlib.Data.Nat.Find
import Mathlib.Order.Atoms
import Mathlib.Data.SetLike.Basic
/-!
# Rooted trees
This file proves... |
ExistUnique.lean | /-
Copyright (c) 2023 Winston Yin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Winston Yin
-/
import Mathlib.Analysis.ODE.Gronwall
import Mathlib.Analysis.ODE.PicardLindelof
import Mathlib.Geometry.Manifold.IntegralCurve.Transform
import Mathlib.Geometry.Manifold.Is... |
MathlibTestExecutable.lean | import Lean
import Std
import Qq
import Batteries
import Aesop
import ProofWidgets
import Mathlib
import Plausible
def main : IO Unit := do
IO.println "Verified that an executable importing all of Mathlib and its upstream dependencies can be built and executed."
|
Forget.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.Topology.Sheaves.Sheaf
/-!
# Checking the sheaf condition on the underlying presheaf of types.
If `G : C ⥤ D` is a functor which reflects isomorphisms an... |
LocallyDirected.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.Limits.Shapes.WidePullbacks
/-!
## Locally directed gluing
We say that a diagram of sets is "locally directed" if for any `V, W ⊆ U` in the ... |
Order.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Heyting.Basic
import Mathlib.Order.Hom.Basic
import Mathlib.Order.WithBot
/-!
# Orders on a sum type
This file defines the disjoint sum and the lin... |
Int.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Emirhan Duysak, Adem Alp Gök, Junyan Xu
-/
import Mathlib.Algebra.Order.Group.Int
import Mathlib.Algebra.Order.Group.Unbundled.Int
import Mathlib.Algebra.Order.Ring.Defs
... |
Exp.lean | /-
Copyright (c) 2025 Janos Wolosz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Janos Wolosz
-/
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.Algebra.BigOperators.GroupWithZero.Action
import Mathlib.Algebra.Module.BigOpe... |
Finite.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.Ideal.IdempotentFG
import Mathlib.RingTheory.Unramified.Basic
import Mathlib.RingTheory.Flat.Stability
/-!
# Various results about unramified alg... |
ZeroDivisorsInAddMonoidAlgebras.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.Algebra.MonoidAlgebra.Defs
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.Data.Finsupp.Lex
import Math... |
Defs.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.Algebra.Order.Group.Unbundled.Int
import Mathlib.Algebra.Order.Nonneg.Basic
import Mathlib.Algebra.Order.Ring.Unbundled.Rat
imp... |
norm_num_ordinal.lean | import Mathlib.Tactic.NormNum.Ordinal
universe u
example : (2 : Ordinal.{0}) * 3 + 4 = 10 := by norm_num
example : ¬(15 : Ordinal.{4}) / 4 % 34 < 3 := by norm_num
example : (12 : Ordinal.{u}) ^ (2 : Ordinal.{u}) ^ (2 : ℕ) ≤
(12 : Ordinal.{u}) ^ (2 : Ordinal.{u}) ^ (2 : ℕ) := by norm_num
|
Extend.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.MeanValue
/-!
# Extending differentiability to the boundary
We investigate how differentiable functions inside a set extend t... |
Lemmas.lean | /-
Copyright (c) 2020 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.Group.Subgroup.ZPowers.Basic
import Mathlib.Data.Countable.Basic
import Mathlib.Data.Int.Cast.Lemmas
import Mathlib.GroupTheory.Subgroup.Centralize... |
LCM.lean | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau
-/
import Mathlib.Data.Nat.Factorization.Basic
import Mathlib.Data.Nat.GCD.BigOperators
/-!
# Lemmas about `factorizationLCMLeft`
This file contains some lemmas about `facto... |
BallSphere.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import Mathlib.Analysis.Normed.Group.Uniform
/-!
# Negation on spheres and balls
In this file we define `InvolutiveNeg` and `ContinuousNeg` insta... |
Factorial.lean | /-
Copyright (c) 2023 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Data.Nat.Factorial.BigOperators
import Mathlib.Data.ZMod.Basic
/-!
# Facts about factorials in ZMod
... |
finmodule.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... |
Hom.lean | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Hom.Basic
import Mathlib.Algebra.GroupWithZero.Basic
/-!
# Monoid with zero and group with zero homomorphisms
This file defines homomorphi... |
nilpotent.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import fintype div bigop prime finset fingroup morphism.
Fro... |
Order.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.Data.Complex.Norm
/-!
# The partial order on the complex numbers
This order is defined by `z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im`.
This is a natural order o... |
MDifferentiable.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Geometry.Manifold.VectorBundle.Basic
import Mathlib.Geometry.Manifold.MFDeriv.NormedSpace
import Mathlib.Geometry.Manifold.MFDeriv.SpecificFuncti... |
AbsolutelyContinuous.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
import Mathlib.Probability.Kernel.Composition.MeasureCompProd
import Mathlib.Probability.Kernel.RadonNikodym
/-!
# Absolute continuity of the compositi... |
FastInstance.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kyle Miller
-/
import Lean.Elab.SyntheticMVars
import Lean
import Mathlib.Init
/-!
# The `fast_instance%` term elaborator
-/
namespace Mathlib.Elab.FastInstance
open Lean ... |
Linear.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.Algebra.Homology.ShortComplex.Preadditive
import Mathlib.CategoryTheory.Linear.LinearFunctor
/-!
# Homology of linear categories
In this file, it is shown that... |
finmodule.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... |
DPMorphism.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, María Inés de Frutos-Fernández
-/
import Mathlib.RingTheory.DividedPowers.Basic
/-! # Divided power morphisms
Let `A` an... |
Profinite.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.Topology.Separation.Regular
import Mathlib.Topology.Connected.TotallyDisconnected
/-!
# Separation properties: profinite spaces
-/
o... |
BesicovitchVectorSpace.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.Covering.Besicovitch
import Mathlib.Tactic.AdaptationNote
import Mathlib.Algeb... |
FreeCommRing.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Johan Commelin
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Logic.Equiv.Functor
import Mathlib.RingTheory.FreeRing
/-... |
FinBoolAlg.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.Fintype.Powerset
import Mathlib.Order.Category.BoolAlg
import Mathlib.Order.Category.FinBddDistLat
import Mathlib.Order.Hom.CompleteLattice
import Mat... |
Nilpotent.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.RingTheory.MvPolynomial.Homogeneous
import Mathlib.RingTheory.Polynomial.Nilpotent
/-!
# Nilpotents and units in multivariate polynomial rings
We prove tha... |
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... |
Basic.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Semisimple.Defs
import Mathlib.Order.BooleanGenerators
/-!
# Semisimple Lie algebras
The famous Cartan-Dynkin-Killing classification of semisim... |
abelian.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import choice div fintype finfun bigop finset prime.
From ma... |
Types.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Monad.Basic
import Mathlib.CategoryTheory.Monad.Kleisli
import Mathlib.CategoryTheory.Category.KleisliCat
import Mathlib.C... |
NonemptyFinLinOrd.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.CategoryTheory.ConcreteCategory.EpiMono
import Mathlib.CategoryTheory.Limits.Shapes.Images
import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
impo... |
interval.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 div fintype bigo... |
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, Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Dynamics.Ergodic.MeasurePreserving
import Mathlib.LinearAlgebra.Determinant
import Mathlib.LinearAlgebra.Matrix.Dia... |
Order.lean | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara, Stefan Kebekus
-/
import Mathlib.Analysis.Analytic.IsolatedZeros
/-!
# Vanishing Order of Analytic Functions
This file defines the order of vanishing of an analytic... |
Defs.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, Johannes Hölzl, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Data.Rat.Init
/-!
# Division (semi)rings and (semi... |
Core.lean | /-
Copyright (c) 2021 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arthur Paulino, Aurélien Saue, Mario Carneiro
-/
import Lean.Elab.PreDefinition.Basic
import Lean.Elab.Tactic.ElabTerm
import Lean.Meta.Tactic.Intro
import Mathlib.Lean.Expr.Basic
impo... |
Ideal.lean | /-
Copyright (c) 2019 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Polynomial.RingDivision
import Mathlib.RingTheory.Adjoin.Polynomial
import Mathlib.RingTheory.Ideal.Maps
/-!
# Ideals in polynomial rings
-/
noncomputa... |
Monotone.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.Analysis.Calculus.Deriv.Slope
import Mathlib.MeasureTheory.Covering.OneDim
import Mathlib.Order.Monotone.Extension
/-!
# Differentiability of mo... |
all_field.v | From mathcomp Require Export algC.
From mathcomp Require Export algebraics_fundamentals.
From mathcomp Require Export algnum.
From mathcomp Require Export closed_field.
From mathcomp Require Export cyclotomic.
From mathcomp Require Export falgebra.
From mathcomp Require Export fieldext.
From mathcomp Require Export fin... |
LinearPMap.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Topology.Algebra.Module.Equiv
import Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness
/-!
# Partial... |
Hyperreal.lean | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir
-/
import Mathlib.Order.Filter.FilterProduct
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Construction of the hyperreal numbers as an ultrapro... |
ZeroObjects.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Johan Commelin
-/
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# Zero objects
A category "has a zero object" if it has an object which is both initial and ter... |
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