filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Ineq.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 Mathlib.Tactic.NormNum.Eq
import Mathlib.Algebra.Order.Field.Defs
import Mathlib.Algebra.Order.Invertible
import Mathlib.Algebra.Order.Monoid.WithTop
import Ma... |
Ring.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.GradedMonoid
import Mathlib.Algebra.DirectSum.Basic
import Mathlib.Algebra.Ring.Associator
/-!
# Additively-graded multiplicative structures on `⨁ i... |
prime.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 path.
From mathcomp Require Import choice fintype div bigop.
(*************************... |
Factors.lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.BigOperators.Ring.List
import Mathlib.Data.Nat.GCD.Basic
import Mathlib.Data.Nat.Prime.Basic
import Ma... |
character.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 choice ssrnat seq.
From mathcomp Require Import path div fintype... |
Functor.lean | /-
Copyright (c) 2016 Leonardo de Moura. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Mathlib.Control.Basic
import Mathlib.Data.Set.Defs
import Mathlib.Data.Set.Lattice.Image
import Mathlib.Data.Set.Notation
/-!
# Functoriality of `Set`
... |
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... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
KAbstractPositions.lean | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
import Mathlib.Init
import Lean.HeadIndex
import Lean.Meta.ExprLens
import Lean.Meta.Check
/-!
# Find the positions of a pattern in an expression
This file def... |
IntegralRestrict.lean | /-
Copyright (c) 2023 Andrew Yang, Patrick Lutz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.RingTheory.DedekindDomain.IntegralClosure
import Mathlib.RingTheory.RingHom.Finite
import Mathlib.RingTheory.Localization.LocalizationLocalizat... |
Basic.lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.Algebra.Group.Hom.Basic
import Mathlib.Logic.Equiv.Basic
import Mathlib.Tactic.... |
Defs.lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Fabian Glöckle, Kyle Miller
-/
import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.LinearAlgebra.Span.Defs
/-!... |
Projective.lean | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, David Swinarski
-/
import Mathlib.Algebra.Module.FinitePresentation
import Mathlib.Algebra.Module.Projective
import Mathlib.LinearAlgebra.Dimension.Constructions
import Mathl... |
PNatToNat.lean | /-
Copyright (c) 2025 Vasilii Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasilii Nesterov
-/
import Mathlib.Data.PNat.Basic
/-!
# `pnat_to_nat`
This file implements the `pnat_to_nat` tactic that shifts `PNat`s in the context to `Nat`.
## Implementation... |
BifunctorHomotopy.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.Homology.Bifunctor
import Mathlib.Algebra.Homology.Homotopy
/-!
# The action of a bifunctor on homological complexes factors through homotopies
Given a... |
TensorProduct.lean | /-
Copyright (c) 2025 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Yunzhou Xie
-/
import Mathlib.Algebra.Central.Basic
import Mathlib.RingTheory.Flat.Basic
import Mathlib.LinearAlgebra.Basis.VectorSpace
/-!
# Lemmas about tensor product... |
LocallyUniformConvergence.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.UniformSpace.UniformConvergence
/-!
# Locally uniform convergence
We define a sequence of functions `Fₙ` to *converge locally uniforml... |
integral_char.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... |
Opposite.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.Algebra.Group.Commute.Defs
import Mathlib.Algebra.Group.InjSurj
import Mathlib.Algebra.Opposites
import Mathlib.Tactic.Spread
/-!
# Group structures on the mult... |
Associated.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, Anne Baanen
-/
import Mathlib.Algebra.BigOperators.Finsupp.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.GroupWithZero.... |
Pointwise.lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
import Mathlib.Algebra.Group.Submonoid.Membership
import Mathlib.Algebra.Order.BigOperators.Group.List
import Mathli... |
Degree.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.Subsemigroup.Operations
import Mathlib.Algebra.MonoidAlgebra.Support
import Mathlib.Order.Filter.Extr
/-!
# Lemmas about the `sup` and `in... |
Enrichment.lean | /-
Copyright (c) 2024 Daniel Carranza. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Carranza, Joël Riou
-/
import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
import Mathlib.CategoryTheory.Closed.Monoidal
/-!
# A closed monoidal category is enriched in itse... |
mxalgebra.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 b... |
Basic.lean | /-
Copyright (c) 2020 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Algebra.Ring.Subring.Defs
import Mathlib.Algebra.Ring.Subsemiring.Bas... |
Multiset.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Data.List.Chain
import Mathlib.Data.Multiset.Sort
import Mathlib.Logic.Equiv.List
/-!
# `Encodable` and `Denumerable` instances for `Multiset`
-/
var... |
Multiset.lean | /-
Copyright (c) 2021 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde, Daniel Weber
-/
import Mathlib.Algebra.BigOperators.Group.Multiset.Defs
import Mathlib.Algebra.Order.BigOperators.GroupWithZero.List
/-!
# Big operators on a m... |
ModuleTopology.lean | /-
Copyright (c) 2024 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Will Sawin
-/
import Mathlib.Topology.Algebra.Module.Equiv
import Mathlib.RingTheory.Finiteness.Cardinality
import Mathlib.Algebra.Algebra.Bilinear
/-!
# A "module topol... |
Basic.lean | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.LinearAlgebra.Countable
import Mathlib.LinearAlgebra.FreeModule.PID
import Mathlib.MeasureTheory.Group.FundamentalDomain
import Mathlib.MeasureTheory.Mea... |
Shrink.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.Order.SuccPred.Basic
import Mathlib.Logic.Small.Defs
/-!
# Order instances on Shrink
If `α : Type v` is `u`-small, we transport various order related
instances... |
Recurse.lean | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth
-/
import Mathlib.Util.AtomM
/-!
# Running `AtomM` metaprograms recursively
Tactics such as `ring` and `abel` are implemented using the `AtomM` monad,... |
Frobenius.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Algebra.ZMod
import Mathlib.Data.Nat.Multiplicity
import Mathlib.FieldTheory.Perfect
import Mathlib.RingTheory.WittVector.Basic
import Mathlib.... |
ssrAC.v | From HB Require Import structures.
From Corelib Require Import PosDef.
(* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *)
(* (the warning was completely removed in 9.0) *)
Set Warnings "-hiding-delimiting-key".
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop.
... |
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... |
Basic.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Floris van Doorn
-/
import Mathlib.Geometry.Manifold.ContMDiff.Defs
/-!
## Basic properties of `C^n` functions between manifolds
In this file, we show that stan... |
Orthogonality.lean | /-
Copyright (c) 2023 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.BigOperators.Expect
import Mathlib.Algebra.Group.AddChar
import Mathlib.Analysis.RCLike.Inner
/-!
# Orthogonality of c... |
Compact.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, Patrick Massot
-/
import Mathlib.Topology.Algebra.Group.Pointwise
import Mathlib.Topology.Sets.Compacts
/-!
# Additional results on topological groups
... |
Grp_.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.Algebra.Category.Grp.Limits
import Mathlib.CategoryTheory.Monoidal.Grp_
/-!
# Yoneda embedding of `Grp_ C`
We show that group objects are exactly those who... |
Defs.lean | /-
Copyright (c) 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Yury Kudryashov
-/
import Mathlib.Tactic.Continuity
import Mathlib.Tactic.Lift
import Mathlib.Topology.Defs.Basic
/-!
# Continuous bundled maps
In this file we de... |
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... |
Basic.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.RingTheory.Norm.Defs
import Mathlib.FieldTheory.PrimitiveElement
import Mathlib.LinearAlgebra.Matrix.Charpoly.Minpoly
import Mathlib.LinearAlgebra.Matrix.ToL... |
Extreme.lean | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Extreme
import Mathlib.Dynamics.Ergodic.Function
import Mathlib.Dynamics.Ergodic.RadonNikodym
import Mathlib.Probability.ConditionalP... |
NonUnitalSubsemiring.lean | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Algebra.Group.Subsemigroup.Basic
import Mathlib.RingTheory.NonUnitalSubsemiring.Basic
import Mathlib.Algebra.S... |
Imo2019Q2.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Geometry.Euclidean.Angle.Sphere
import Mathlib.Geometry.Euclidean.Sphere.SecondInter
/-!
# IMO 2019 Q2
In triangle `ABC`, point `A₁` lies on side `BC` an... |
Rel.lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Data.Set.BooleanAlgebra
/-!
# Relations as sets of pairs
This file provides API to regard relations between `α` and `β` as sets of pairs `Set (α × β)`... |
Limits.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Limits.Creates
/-!
# Adjunctions and limits
A left adjoint preserves colimits... |
StarRingHom.lean | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Algebra.Ring.Defs
import Mathlib.Algebra.Star.Basic
/-!
# Morphisms of star rings
This file defines a new type of morphism between (non-unita... |
Basic.lean | /-
Copyright (c) 2016 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Data.Set.Defs
import Mathlib.Logic.Basic
import Mathlib.Logic.ExistsUnique
import Mathlib.Logic.Nonempty
import Mathlib.Logic.Nontrivia... |
Integral.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.Algebra.GroupWithZero.NonZeroDivisors
import Mathlib.Algebra.Polynomial.Lifts
import Mathlib.Ring... |
Basic.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Bhavik Mehta
-/
import Mathlib.CategoryTheory.Equivalence
import Mathlib.CategoryTheory.Yoneda
/-!
# Adjunctions between functors
`F ⊣ G` represents the dat... |
Basic.lean | /-
Copyright (c) 2024 Frédéric Marbach. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Marbach
-/
import Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.Lie.Subalgebra
import Mathlib.RingTheory.Nilpo... |
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... |
AffineTransitionLimit.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.AlgebraicGeometry.IdealSheaf.Functorial
import Mathlib.AlgebraicGeometry.Morphisms.Separated
import Mathlib.CategoryTheory.Filtered.Final
/-!
# Inverse lim... |
Prod.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.LinearAlgebra.Prod
import Mathlib.RingTheory.Finiteness.Defs
/-!
# Finitely generated product (sub)modules
-/
open Function (Surjective)
open Finsup... |
all.v | From mathcomp Require Export all_boot.
From mathcomp Require Export all_order.
From mathcomp Require Export all_fingroup.
From mathcomp Require Export all_algebra.
From mathcomp Require Export all_solvable.
From mathcomp Require Export all_field.
From mathcomp Require Export all_character.
|
SpecialLinearGroup.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Wen Yang
-/
import Mathlib.LinearAlgebra.Matrix.Adjugate
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.Matrix.Transvection
import Mathlib.RingTheory.... |
SemiNormedGrp.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Riccardo Brasca
-/
import Mathlib.Analysis.Normed.Group.Constructions
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms... |
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... |
Find.lean | import Mathlib.Tactic.Find
theorem add_comm_zero {n} : 0 + n = n + 0 := Nat.add_comm _ _
-- These results are too volatile to test with `#guard_msgs`,
-- we just suppress them for now.
#guard_msgs (drop info) in
#find _ + _ = _ + _
#guard_msgs (drop info) in
#find ?n + _ = _ + ?n
#guard_msgs (drop info) in
#find (_... |
generic_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 choice.
From mathcomp Require Import seq fintype.
(*****... |
FiniteInfinite.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Data.DFinsupp.Defs
import Mathlib.Data.Fintype.Pi
/-!
# Finiteness and infiniteness of the `DFinsupp` type
## Main results
* `DFinsupp.fintype... |
Homogeneous.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Wieser
-/
import Mathlib.Algebra.DirectSum.Internal
import Mathlib.Algebra.GradedMonoid
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Algebra.MvPolyn... |
NReflectsIso.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.FunctorN
import Mathlib.AlgebraicTopology.DoldKan.Decomposition
import Mathlib.CategoryTheory.Idempotents.HomologicalComplex
import Mat... |
Finiteness.lean | /-
Copyright (c) 2023 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Tactic.Positivity.Core
/-!
# Finiteness tactic
This file implements a basic `finiteness` tactic, designed to solve goals of the form `*** < ∞` and
... |
Basic.lean | /-
Copyright (c) 2025 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson, Jun Kwon
-/
import Mathlib.Data.Set.Basic
import Mathlib.Data.Sym.Sym2
/-!
# Multigraphs
A multigraph is a set of vertices and a set of edges,
together with incidence dat... |
WithDensity.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.Integral.Bochner.ContinuousLinearMap
import Mathlib.Probability.Kernel.MeasurableLIntegral
/-!
# With Density
For an s-finite kernel `κ : K... |
Init.lean | /-
Copyright (c) 2023 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Mathlib.Init
import Aesop
/-!
# Continuity Rule Set
This module defines the `Continuous` Aesop rule set which is used by the
`continuity` tactic. Aesop rule... |
NthRewrite.lean | import Mathlib.Tactic.NthRewrite
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Vector.Defs
import Mathlib.Algebra.Ring.Nat
set_option autoImplicit true
open Mathlib
example [AddZeroClass G] {a : G} (h : a = a): a = (a + 0) := by
nth_rewrite 2 [← add_zero a] at h
exact h
example [AddZeroClass G] {a : G} ... |
Wallis.lean | /-
Copyright (c) 2021 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang
-/
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
/-! # The Wallis formula for Pi
This file establishes the Wallis product for `π` (`Real.tendsto_prod_pi_div_t... |
ContinuousMap.lean | /-
Copyright (c) 2025 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.ContinuousMap.Compact
import Mathlib.Topology.ContinuousMap.Algebra
import Mathlib.MeasureTheory.Integral.IntegrableOn
/-!
# Specific res... |
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... |
Block.lean | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.Data.Matrix.Composition
import Mathlib.Data.Matrix.ConjTranspose
/-!... |
finset_builder.lean | import Mathlib.Order.Interval.Finset.Basic
/-!
# Examples of finset builder notation
-/
open Finset
variable {α : Type*} (p : α → Prop) [DecidablePred p]
/-! ## `Data.Finset.Basic` -/
example (s : Finset α) : {x ∈ s | p x} = s.filter p := rfl
/-! ## `Data.Fintype.Basic` -/
section Fintype
variable [Fintype α]
e... |
Sinc.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.Analysis.SpecialFunctions.Trigonometric.Sinc
import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic
import Mathlib.MeasureTheory.Function.L1Space.Int... |
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... |
Rfl.lean | /-
Copyright (c) 2022 Newell Jensen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Newell Jensen
-/
import Mathlib.Init
import Lean.Meta.Tactic.Rfl
/-!
# `Lean.MVarId.liftReflToEq`
Convert a goal of the form `x ~ y` into the form `x = y`, where `~` is a reflexive
re... |
falgebra.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... |
HasLaw.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: EtienneMarion
-/
import Mathlib.Probability.Density
import Mathlib.Probability.Moments.Variance
/-!
# Law of a random variable
We introduce a predicate `HasLaw X μ P` stating that th... |
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, Mario Carneiro, Patrick Massot
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Order.Filter.Tendsto
import Mathlib.Tactic.Monotonicity.Basic
import Mathlib.Topology... |
Monovary.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.Data.Set.Operations
import Mathlib.Order.Lattice
/-!
# Monovariance of functions
Two functions *vary together* if a strict change in the first implies a ... |
LineGraph.lean | /-
Copyright (c) 2024 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.Combinatorics.SimpleGraph.Basic
/-!
# LineGraph
## Main definitions
* `SimpleGraph.lineGraph` is the line graph of a simple graph `G`, with vertices as ... |
Bounded.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.GroupTheory.GroupAction.Pointwise
import Mathlib.Analysis.LocallyConvex.Basic
import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
import Mathlib.Analysis.... |
Units.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Algebra.Order.Ring.Abs
/-!
# Lemmas about units in `ℤ`, which interact with the order structure.
-/
namespace Int
theorem isUnit_iff_abs_eq {x : ℤ} :... |
GodelBetaFunction.lean | /-
Copyright (c) 2023 Shogo Saito. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shogo Saito. Adapted for mathlib by Hunter Monroe
-/
import Mathlib.Data.Nat.ModEq
import Mathlib.Data.Nat.ChineseRemainder
import Mathlib.Data.Nat.Prime.Defs
import Mathlib.Data.Nat.Pai... |
Invertible.lean | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
import Mathlib.Algebra.MvPolynomial.Basic
import Mathlib.RingTheory.AlgebraTower
/-!
# Invertible polynomials
This file is a stub ... |
DoubleFactorial.lean | /-
Copyright (c) 2023 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.Ring
import Mathlib.Tactic.Positivity.Core
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# D... |
Action.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.Algebra.BigOperators.Finprod
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Algebra.Order.Group.Multiset
import Mathlib.Data.Finset.... |
Derivation.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Algebra.MvPolynomial.Supported
import Mathlib.RingTheory.Derivation.Basic
/-!
# Derivations of multivariate polynomials
In this file we prove that ... |
Inv.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.Deriv.Mul
import Mathlib.Analysis.Calculus.Deriv.Comp
/-!
# Derivatives of `x ↦ x⁻¹` and `f x / g x`
In this... |
Fibration.lean | /-
Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Sara Rousta
-/
import Mathlib.Order.UpperLower.Basic
/-!
# Upper/lower sets and fibrations
-/
open Set
namespace Relation
variable {α β : Type*} {f : α → β... |
ReflectsPrecoherent.lean | /-
Copyright (c) 2024 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EffectiveEpi.Enough
import Mathlib.CategoryTheory.EffectiveEpi.Preserves
import Mathlib.CategoryTheory.Sites.Coherent.CoherentTopolo... |
SymmDiff.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.Order.BooleanAlgebra.Set
import Mathlib.Order.SymmDiff
/-! # Symmetric differences of sets -/
assert_not_exists RelIso
namespace Se... |
Pow.lean | /-
Copyright (c) 2015 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Yury Kudryashov
-/
import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
import Mathlib.Algebra.Order.Monoid.Unbundled.OrderDual
import Mathlib.Tactic.Lift... |
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... |
Defs.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, Anne Baanen
-/
import Mathlib.LinearAlgebra.Quotient.Defs
import Mathlib.RingTheory.Congruence.Defs
import Mathlib.RingTheory.Ideal.Defs
/-!
# Idea... |
SurjectiveOnStalks.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.AlgebraicGeometry.Morphisms.RingHomProperties
import Mathlib.RingTheory.RingHom.Surjective
import Mathlib.RingTheory.Spectrum.Prime.TensorProduct
import Math... |
EpiMono.lean | /-
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.EpiMono
import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
import Mathlib.CategoryTheory.LiftingProperties.Adjunction
/-!
# Preservati... |
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... |
Defs.lean | /-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Order.Monoid.Unbundled.Basic
import Mathlib.Order.Lattice
/-!
# Ordered Subtraction
This file proves l... |
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... |
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