filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Union.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.Interval.Set.LinearOrder
/-!
# Monotonicity on intervals
In this file we prove that a fu... |
Lemmas.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best
-/
import Mathlib.Algebra.BigOperators.Group.List.Basic
import Mathlib.Algebra.Divisibility.Basic
import Mathlib.Algeb... |
Array.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Vector.Basic
import Mathlib.Logic.Equiv.List
/-!
# Equivalences involving `Array`
-/
namespace Equiv
/-- The natural equivalence between array... |
Basic.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Logic.Encodable.Pi
/-!
# W types
Given `α : Type` and `β : α → Type`, the W type determined by this data, `WTyp... |
RelClasses.lean | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yury Kudryashov
-/
import Mathlib.Logic.IsEmpty
import Mathlib.Order.Basic
import Mathlib.Tactic.MkIffOfInductiveProp
import Batteries.WF
/-!
# Unbundled... |
LocallyFullyFaithful.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.CategoryTheory.Sites.LocallySurjective
/-!
# Locally fully faithful functors into sites
## Main results
- `CategoryTheory.Functor.IsLocallyFull`:
A func... |
Delete.lean | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Loop
/-!
# Matroid Deletion
For `M : Matroid α` and `X : Set α`, the *deletion* of `X` from `M` is the matroid `M ＼ X`
with ground set `M.E ... |
NatDivisors.lean | /-
Copyright (c) 2023 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Yury Kudryashov
-/
import Mathlib.NumberTheory.Divisors
import Mathlib.Algebra.Group.Pointwise.Finset.Basic
/-!
# `Nat.divisors` as a multiplicative homomorpism
The ma... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
AffineAnd.lean | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
import Mathlib.AlgebraicGeometry.Morphisms.Affine
import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
/-!
# Affine morphisms with additional ring hom pr... |
Field.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.Algebra.Order.Module.Defs
import Mathlib.Algebra.Field.Defs
import Mathlib.Tactic.Positivity.Core
/-!
# Ordered vector spaces
-/
open OrderDual
variable... |
Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Commute.Units
import Mathlib.Algebra.Group.Invertible.Basic
import Mathlib.Logic.Basic
import Mathlib.Data.Set.Basic
import Math... |
Term.lean | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
import Mathlib.Init
import Lean.Elab.SyntheticMVars
/-!
# Additions to `Lean.Elab.Term`
-/
namespace Lean.Elab.Term
/-- Fully elaborates the term `patt`, allowing typecl... |
Quotient.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Johan Commelin, Patrick Massot
-/
import Mathlib.RingTheory.Ideal.Quotient.Operations
import Mathlib.RingTheory.Valuation.Basic
/-!
# The valuation on a quotient ring
... |
GlueData.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.Tactic.CategoryTheory.Elementwise
import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
impor... |
perm.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 tup... |
Center.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jireh Loreaux
-/
import Mathlib.Algebra.Group.Center
import Mathlib.Algebra.GroupWithZero.Units.Basic
/-!
# Center of a group with zero
-/
assert_not_exists RelIso Finset R... |
CompProdEqIff.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.Probability.Kernel.Composition.AbsolutelyContinuous
/-!
# Condition for two kernels to be equal almost everywhere
We prove that two finite kernels `κ, η ... |
matrix.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 finfun f... |
Limits.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.Limits
import Mathlib.Algebra.Category.ModuleCat.Sheaf
import Mathlib.CategoryTheory.Sites.Limits
/-! # Limits in categories... |
Defs.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Group.Equiv.Opposite
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.BigOperators.Group.Multiset.Defs
import Mathlib.Data.Fi... |
Set.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Data.Set.Image
/-!
### Recursion on the natural numbers and `Set.range`
-/
namespace Nat
section Set
open Set
theorem zero_union_range_succ : {... |
apply_rules.lean | import Mathlib.Algebra.Order.Field.Basic
set_option autoImplicit true
open Nat
example {a b c d e : Nat} (h1 : a ≤ b) (h2 : c ≤ d) (h3 : 0 ≤ e) :
a + c * e + a + c + 0 ≤ b + d * e + b + d + e :=
Nat.add_le_add (Nat.add_le_add (Nat.add_le_add
(Nat.add_le_add h1 (Nat.mul_le_mul_right _ h2)) h1) h2) h3
exampl... |
Ideal.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.GroupTheory.MonoidLocalization.Away
import Mathlib.RingTheory.Ideal.Quotient.Operations
import Ma... |
IntermediateValue.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Alistair Tucker, Wen Yang
-/
import Mathlib.Order.Interval.Set.Image
import Mathlib.Order.CompleteLatticeIntervals
import Mathlib.Topology.Order.DenselyOrdered
import... |
jordanholder.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 big... |
Constructors.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.AlgebraicGeometry.Morphisms.Basic
import Mathlib.RingTheory.RingHomProperties
/-!
# Constructors for properties of morphisms between schemes
This file pro... |
Cardinality.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.GroupTheory.MonoidLocalization.Cardinality
import Mathlib.RingTheory.OreLocalization.Cardinality
/... |
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... |
Faces.lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.AlgebraicTopology.DoldKan.Homotopies
import Mathlib.Tactic.Ring
/-!
# Study of face maps for the Dold-Kan correspondence
In this file, we obtain the technical... |
AddChar.lean | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Algebra.Group.AddChar
import Mathlib.Topology.DenseEmbedding
/-!
# Additive characters of topological monoids
-/
lemma DenseRange.addChar_eq_of_eval_... |
fintype.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 ssrnotations eqtype.
From mathcomp Require Import ssrnat seq choice pat... |
Add.lean | /-
Copyright (c) 2019 Gabriel Ebner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gabriel Ebner, Sébastien Gouëzel, Yury Kudryashov, Anatole Dedecker
-/
import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Add
/-!
# One-dimensional de... |
Enumerate.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Tactic.Common
import Mathlib.Data.Set.Insert
/-!
# Set enumeration
This file allows enumeration of sets given a ... |
RatLemmas.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.Topology.Instances.Irrational
import Mathlib.Topology.Instances.Rat
import Mathlib.Topology.Compactification.OnePoint.Basic
import Mathlib.Topology.M... |
BoolAlg.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.HeytAlg
import Mathlib.Order.Hom.CompleteLattice
/-!
# The category of boolean algebras
This defines `BoolAlg`, the category of boolean al... |
ssralg.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 choice fintype finf... |
CharP.lean | /-
Copyright (c) 2023 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Algebra.CharP.Basic
import Mathlib.ModelTheory.Algebra.Ring.FreeCommRing
import Mathlib.ModelTheory.Algebra.Field.Basic
/-!
# First order theory of field... |
Finite.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.Data.Fintype.Defs
/-!
# Finite types with addition/multiplications
This file contains basic results and insta... |
Finset.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Ring.Pointwise.Set
import Mathlib.Algebra.Ring.InjSurj
import Mathlib.Algebra.Group.Pointwise.Finset.Basic
/-!
# Pointwise operations of sets in a... |
fieldext.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 div.
From mathcomp Require Import choice fintype tupl... |
StarOrder.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.InnerProductSpace.Positive
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic
import Mathlib.Analysis.CStarAlgebra.Continuo... |
LinearMap.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo, Yury Kudryashov, Frédéric Dupuis,
Heather Macbeth
-/
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.Topology.Algebra.Co... |
ClopenNhdofOne.lean | /-
Copyright (c) 2024 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan, Yi Song, Xuchun Li
-/
import Mathlib.GroupTheory.Index
import Mathlib.Topology.Algebra.Group.ClosedSubgroup
import Mathlib.Topology.Algebra.OpenSubgroup
import Mathlib.Topolo... |
Measurable.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.Analysis.Calculus.LineDeriv.Basic
import Mathlib.Analysis.Calculus.FDeriv.Measurable
/-! # Measurability of the line derivative
We prove in `me... |
matrix.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 finfun f... |
Pointwise.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.Group.Pointwise.Set.Scalar
import Mathlib.Algebra.Order.Module.Field
import Mathlib.Order.Bounds.OrderIso
import Mathlib.Order.GaloisConnection.Bas... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Cases.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Lean.Elab.Tactic.Induction
import Batteries.Tactic.OpenPrivate
import Mathlib.Lean.Expr.Basic
import Batteries.Data.List.Basic
/-!
# Backward compatible imple... |
CharAndCard.lean | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Algebra.CharP.Basic
import Mathlib.Algebra.CharP.Lemmas
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# Charac... |
Inner.lean | /-
Copyright (c) 2023 Yaël Dilies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dilies
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# L2 inner product of finite sequences
This file defines the weighted L2 inner product of functions `f g : ι → R` where... |
HittingTime.lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
import Mathlib.Probability.Process.Stopping
import Mathlib.Tactic.AdaptationNote
/-!
# Hitting time
Given a stochastic process, the hitting time provides th... |
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... |
div.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.
(******************************************************************************)
(* Th... |
FlagRange.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Order.Fin.Basic
import Mathlib.Order.Preorder.Chain
/-!
# Range of `f : Fin (n + 1) → α` as a `Flag`
Let `f : Fin (n + 1) → α` be an `(n + 1)`-tupl... |
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 ssrnat seq div.
From mathcomp Require Import choice fintype prim... |
Seq.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.Option.NAry
import Mathlib.Data.Seq.Computation
/-!
# Possibly infinite lists
This file provides a `Seq α` type representing possibly infinite l... |
Disjointed.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yaël Dillies, David Loeffler
-/
import Mathlib.Order.PartialSups
import Mathlib.Order.Interval.Finset.Fin
/-!
# Making a sequence disjoint
This file defines the way t... |
qfpoly.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple div bigop binomial finset finfun.
From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm.
From mathcomp Require Import fingroup falgebra fiel... |
SigmaCompact.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.Topology.Bases
import Mathlib.Topology.Compactness.LocallyCompact
import Mathlib.Topology.Compactness.LocallyFinite
/... |
Defs.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Group.List.Defs
import Mathlib.Algebra.Group.Basic
import Mathlib.Data.Multiset.Basic
import Mathlib.Data.Multiset.Filter
... |
JacobsonNoether.lean | /-
Copyright (c) 2024 F. Nuccio, H. Zheng, W. He, S. Wu, Y. Yuan, W. Jiao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Huanyu Zheng, Sihan Wu, Wanyi He, Weichen Jiao, Yi Yuan
-/
import Mathlib.Algebra.Central.Defs
import Mathlib.Algebra.CharP.L... |
RegularMono.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
import Mathlib.CategoryTheory.Limits.... |
ChangeOfRings.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
import Mathlib.Algebra.Category.ModuleCat.Presheaf.ChangeOfRings
import Mathlib.CategoryTheory.Sites.LocallySurjective
/-!
# Ch... |
ConjFinite.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Algebra.Group.Conj
import Mathlib.Data.Fintype.Units
/-!
# Conjugacy of elements of finite groups
-/
assert_not_exists Field
-- TODO: the following ... |
InjSurj.lean | /-
Copyright (c) 2014 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
-/
import Mathlib.Algebra.Order.Ring.InjSurj
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module (sin... |
gproduct.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 bigo... |
FilterProduct.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, Yury Kudryashov
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Order.Filter.Ring
import Mathli... |
numfield.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... |
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... |
Imo2024Q6.lean | /-
Copyright (c) 2024 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Data.Rat.Floor
import Mathlib.SetTheory.Cardinal.Basic
/-!
# IMO 2024 Q6
A function `f: ℚ → ℚ` is called *aquaesulian* if the following
property holds: f... |
finalg.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 finset f... |
RefinedDiscrTree.lean | import Mathlib.Lean.Meta.RefinedDiscrTree.Encode
import Mathlib
open Qq Lean Meta RefinedDiscrTree
macro "#log_keys" e:term : command =>
`(command| run_meta do
for keys in ← encodeExprWithEta (labelledStars := true) q($e) do
logInfo m! "{← keysAsPattern keys}")
-- eta reduction:
/-- info: Int.succ -/
#gu... |
DualNumber.lean | import Mathlib.Algebra.DualNumber
open DualNumber
-- TODO(kmill): make a ToExpr instance for DualNumber
set_option eval.pp false
/-- info: 0 + 0*ε -/
#guard_msgs in
#eval (0 : ℕ[ε])
/-- info: 2 + 0*ε -/
#guard_msgs in
#eval (2 : ℕ[ε])
/-- info: 6 + 0*ε -/
#guard_msgs in
#eval (2 + 4 : ℕ[ε])
/-- info: 2 + 0*ε + (0... |
CompareReals.lean | /-
Copyright (c) 2019 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Topology.Instances.Rat
import Mathlib.Topology.UniformSpace.AbsoluteValue
import Mathlib.Topology.UniformSpace.Completion
/-!
# Comparison of Cauchy r... |
UnitInterval.lean | /-
Copyright (c) 2024 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Gaëtan Serré
-/
import Mathlib.MeasureTheory.Measure.Haar.Unique
/-!
# The canonical measure on the unit interval
This file provides a `MeasureTheory.MeasureSpace` instance... |
Subgroup.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Algebra.Group.Subgroup.Defs
import Mathlib.Analysis.Normed.Group.Basic
/-!
# Subgroups of normed (semi)groups
In this f... |
Lemmas.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Even
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Notation.Suppor... |
Filter.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, Jeremy Avigad
-/
import Mathlib.Topology.Defs.Basic
import Mathlib.Data.Setoid.Basic
import Mathlib.Order.Filter.Defs
import Mathlib.Tactic.IrreducibleD... |
Basic.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, Filippo A. E. Nuccio, Riccardo Brasca
-/
import Mathlib.CategoryTheory.Extensive
import Mathlib.CategoryTheory.Sites.Coverage
import Mathlib.CategoryTheory.Ef... |
Notation.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.Tactic.TypeStar
import Mathlib.Tactic.ToAdditive
/-!
# Notations for operations involving order and algebraic structure
## Notations
* `a⁺ᵐ = a ⊔ 1`: ... |
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) 2025 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yunzhou Xie, Jujian Zhang
-/
import Mathlib.Algebra.Category.AlgCat.Basic
import Mathlib.Algebra.Central.Defs
import Mathlib.LinearAlgebra.FiniteDimensional.Defs
import Mathlib.LinearAlge... |
Etale.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.RingHom.Smooth
import Mathlib.RingTheory.RingHom.Unramified
/-!
# Etale ring homomorphisms
We show the meta properties of étale morphi... |
Degree.lean | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.RatFunc.AsPolynomial
import Mathlib.RingTheory.EuclideanDomain
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.RingTheory.Poly... |
Stieltjes.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov, Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Constructions.BorelSpace.Order
import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
import... |
MDifferentiable.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence
import Mathlib.Analysis.Complex.UpperHalfPlane.Manifold
import Mathlib.Analysis.Complex.... |
matrix.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 finfun f... |
Tilted.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.Measure.Decomposition.RadonNikodym
/-!
# Exponentially tilted measures
The exponential tilting of a measure `μ` on `α` by a function `f : α... |
Segment.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Algebra.Order.Invertible
import Mathlib.Algebra.Order.Module.OrderedSMul
import Mathlib.LinearAlgebra.AffineSpac... |
ssralg.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 choice fintype finf... |
Mono.lean | /-
Copyright (c) 2018 Kim Morrison. 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.Iso
/-!
# Pullbacks and monomorphisms
This file provides some results about interactions between pull... |
Center.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.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic
/-!
# Half braidings and the Drinfeld center of a monoidal c... |
fieldext.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 div.
From mathcomp Require Import choice fintype tupl... |
simp_intro.lean | import Mathlib.Tactic.SimpIntro
set_option autoImplicit true
example : x + 0 = y → x = y := by simp_intro h₁
example : x + 0 ≠ y → x ≠ y := by simp_intro h₁ h₂ -- h₂ is bound but not needed
example : x + 0 ≠ y → x ≠ y := by simp_intro h₁ h₂ h₃ -- h₃ is not bound
example (h : x = z) : x + 0 = y → x = z := by simp_int... |
Writer.lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Edward Ayers
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Logic.Equiv.Defs
/-!
# Writer monads
This file introduces monads for managing immutable, appendab... |
Semisimple.lean | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
import Mathlib.LinearAlgebra.Semisimple
/-!
# Semisimple operators on inner product spaces
This file is a p... |
Mirror.lean | /-
Copyright (c) 2020 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.Polynomial.Reverse
/-!
# "Mirror" of a univariate polynomial
In this file we define `Po... |
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.Generator.Basic
import Mathlib.CategoryTheory.Limits.Indization.Category
import Mathlib.CategoryTheory.Preadditive.Indization
/-!
# Separ... |
alt.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice.
From mathcomp Require Import div fintype tupl... |
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