filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
FiniteDimensional.lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Data.Complex.Cardinality
import Mathlib.Data.Complex.Modu... |
MulOpposite.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Jujian Zhang
-/
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Submonoid.Basic
/-!
# Submonoid of opposite monoids
For every monoid `M`, we construct an... |
InnerProductSpace.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.InnerProductSpace.Orientation
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
/-!
# Volume forms and measures on inner product spa... |
TranscendenceBasis.lean | /-
Copyright (c) 2021 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.Matroid.IndepAxioms
import Mathlib.Data.Matroid.Rank.Cardinal
import Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra
import Mathlib.RingTheory.Al... |
UnusedTacticExtension.lean | /-
Copyright (c) 2025 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and module docstring.
import Mathlib.Tactic.Linter.Header
/-!
This file defi... |
HaveLetLinter.lean | /-
Copyright (c) 2024 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Init
import Lean.Elab.Command
import Lean.Server.InfoUtils
import Mathlib.Tactic.DeclarationNames
/-!
# The `have` vs `let` linter
The `have` vs `let... |
SetIntegral.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Integral.Bochner.Set
import Mathlib.Probability.Kernel.Integral
/-! # Integral against a kernel over a set
This file contains lemmas ab... |
Limits.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.Preadditive.Yoneda.Basic
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.CategoryTheory.Limits.Yoneda
/-!
# The Yoneda e... |
mxpoly.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 div fintype tupl... |
Defs.lean | /-
Copyright (c) 2022 Anand Rao, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anand Rao, Rémi Bottinelli
-/
import Mathlib.CategoryTheory.CofilteredSystem
import Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
import Mathlib.Data.Finite.Set
... |
preorder.v | (* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import path fintype tup... |
Opposite.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Group.Opposite
import Mathlib.Algebra.Order.Ring.Defs
import Mathlib.Algebra.Ring.Opposite
/-!
# Ordered ring instances for `MulOpposite`/`A... |
Transform.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.Geometry.Manifold.IntegralCurve.Basic
/-!
# Translation and scaling of integral curves
New integral curves may be constructed by translating or scaling the... |
Subobject.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.Abelian.GrothendieckAxioms.Colim
import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic
import Mathlib.CategoryTheory.Presentable.IsCard... |
UnivLE.lean | /-
Copyright (c) 2023 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Logic.UnivLE
import Mathlib.SetTheory.Ordinal.Basic
/-!
# UnivLE and cardinals
-/
noncomputable section
universe u v
open Cardinal
theorem univLE_iff_cardin... |
Fin.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.GroupTheory.Perm.Cycle.Type
import Mathlib.GroupTheory.Perm.Option
import Mathlib.Logic.Equiv.Fin.Rotate
import Mathlib.Logic.Equiv.Fintype
/-!
# Permutatio... |
CompleteLinearOrder.lean | /-
Copyright (c) 2023 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
import Mathlib.Order.ConditionallyCompleteLattice.Indexed
import Mathlib.Order.SuccPred.Limit
/-!
# Relation between `IsSuccPrelimit` and `iSup` in (conditionally) comple... |
Lemmas.lean | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.GroupWithZero.Divisibility
import Mathlib.Algebra.Ring.Divisibility.Basic
import Mathlib.Data.Nat.Choose.Sum
import Mathlib.GroupTheory.GroupAction.R... |
ssrbool.v | From mathcomp Require Import ssreflect ssrfun.
From Corelib Require Export ssrbool.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(**********************)
(* not yet backported *)
(**********************)
Lemma homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT]
[aP : pred ... |
SmoothNumbers.lean | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Ralf Stephan
-/
import Mathlib.Data.Nat.Factorization.Defs
import Mathlib.Data.Nat.Squarefree
/-!
# Smooth numbers
For `s : Finset ℕ` we define the set `Nat.factoredNum... |
Adjunction.lean | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel, Joël Riou
-/
import Mathlib.CategoryTheory.Shift.CommShift
import Mathlib.CategoryTheory.Adjunction.Mates
/-!
# Adjoints commute with shifts
Given categories `C` and `D` ... |
Real.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Data.ENNReal.Basic
/-!
# Maps between real and extended non-negative real numbers
This file focuses on the functions `ENNReal.toReal... |
Monic.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Algebra.Regular.SMul
/-!
# Theory of monic polynomials
We give se... |
Lattice.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.Finset.Max
import Mathlib.Data.Fintype.Basic
/-!
# Lemmas relating fintypes and order/lattice structure.
-/
open Function
open Nat
universe u... |
SuccPred.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.Group.Nat
import Mathlib.Algebra.Ring.Nat
import Mathlib.Algebra.Order.Monoid.Unbundled.WithTop
import Mathlib.Algebra.Order.Sub.Unbundled.Ba... |
DirectLimit.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Module.LinearMap.Defs
import Mathlib.Data.Rat.Cast.Defs
import Mathlib.Order.DirectedInverseSystem
import Mathlib.Tactic.SuppressCompilation
/-!
# Direc... |
Covering.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Topology.IsLocalHomeomorph
import Mathlib.Topology.FiberBundle.Basic
/-!
# Covering Maps
This file defines covering maps.
## Main definitions
* `... |
Restriction.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.Embedding.Basic
import Mathlib.Algebra.Homology.Additive
/-!
# The restriction functor of an embedding of complex shapes
Given `c` and `c'` co... |
burnside_app.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
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... |
Specialization.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.Order.Category.Preord
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.ContinuousMap.Basic
import Mathlib.Topology.Order.UpperLowerSet... |
Continuous.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou, Andrew Yang
-/
import Mathlib.CategoryTheory.Sites.IsSheafOneHypercover
/-!
# Continuous functors between sites.
We define the notion of continuous functor between sites: these... |
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, Kenny Lau, Johan Commelin, Mario Carneiro, Kevin Buzzard,
Amelia Livingston, Yury Kudryashov
-/
import Mathlib.Algebra.Group.Hom.Defs
import Mathlib.Algebra.Group.Submo... |
Lattice.lean | /-
Copyright (c) 2021 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
import Mathlib.Topology.Constructions
import Mathlib.Topology.Order.OrderClosed
/-!
# Topological lattices
In this file we define mixin classes `ContinuousI... |
T5.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.Order.Interval.Set.OrdConnectedComponent
import Mathlib.Topology.Order.Basic
import Mathlib.Topology.Separation.Regular
/-!
# Linear order is a comp... |
Factorisation.lean | /-
Copyright (c) 2023 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
import Mathlib.CategoryTheory.Category.Basic
import Mathlib.CategoryTheory.Comma.Arrow
import Mathlib.CategoryTheory.Limits.Shapes.Terminal
/-!
# The Factorisati... |
Defs.lean | /-
Copyright (c) 2018 Mitchell Rowett. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Rowett, Kim Morrison
-/
import Mathlib.Algebra.Quotient
import Mathlib.Algebra.Group.Action.Opposite
import Mathlib.Algebra.Group.Subgroup.MulOpposite
import Mathlib.GroupThe... |
Opposite.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.Equiv.Defs
import Mathlib.Algebra.Group.Opposite
import Mathlib.Algebra.Group.Units.Defs
/-!
# Units in multiplicative and additive opposites
... |
Condexp.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.Probability.Kernel.Composition.MeasureComp
import Mathlib.Probability.Kernel.CondDistrib
import Mathlib.Probability.ConditionalProbability
/-!
# Kernel as... |
finfun.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype tuple.
... |
DocString.lean | import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.Linter.DocString
/-! Tests for the `docstring` linter -/
set_option linter.style.docString true
#adaptation_note /--This comment is not inspected by the `docString` linter.-/
example : True := by
#adaptation_note /-- This comment is not inspected by the... |
LinearDisjoint.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.Algebra.Subalgebra.MulOpposite
import Mathlib.Algebra.Algebra.Subalgebra.Rank
import Mathlib.Algebra.Polynomial.Basis
import Mathlib.LinearAlgebra.Basis.Vector... |
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... |
Basic.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.Logic.Equiv.Set
import Mathlib.Order.Interval.Set.OrderEmbedding
import Mathlib.Order.SetNotation
import Mathlib.Order.WellFounde... |
UnitizationL1.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.Algebra.Algebra.Unitization
import Mathlib.Analysis.Normed.Lp.ProdLp
/-! # Unitization equipped with the $L^1$ norm
In another file, the `Unitization �... |
WithTerminal.lean | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith, Adam Topaz
-/
import Mathlib.CategoryTheory.WithTerminal.Basic
deprecated_module (since := "2025-04-10")
|
DeclarationNames.lean | /-
Copyright (c) 2024 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Moritz Firsching
-/
import Lean.DeclarationRange
import Lean.ResolveName
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and... |
automorphism.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 finset fingroup perm morphism.
(*********************... |
PUnit.lean | /-
Copyright (c) 2018 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.Functor.Const
import Mathlib.CategoryTheory.Discrete.Basic
/-!
# The category `Discrete PUnit`
We define `star : C ⥤ Discret... |
Category.lean | /-
Copyright (c) 2017 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tim Baumann, Stephen Morgan, Kim Morrison, Floris van Doorn
-/
import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Iso
/-!
# The category of functors and natural transf... |
norm_num_flt.lean | import Mathlib.Tactic.NormNum
-- From https://leanprover.zulipchat.com/#narrow/channel/113488-general/topic/Proving.20FLT.20with.20norm_num/near/429746342
variable (ignore_me_please : ∀ a b c n : ℕ, a ^ n + b ^ n ≠ c ^ n)
-- previously this proof would work!
/--
error: unsolved goals
n : ℕ
hn : n > 2
a b c : ℕ
⊢ ¬a ... |
UniformIntegrable.lean | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.MeasureTheory.Function.ConvergenceInMeasure
import Mathlib.MeasureTheory.Function.L1Space.Integrable
/-!
# Uniform integrability
This file contains the def... |
Sections.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.Data.Multiset.Bind
/-!
# Sections of a multiset
-/
assert_not_exists Ring
namespace Multiset
variable {α : Type*}
section Sections
/-- The sectio... |
ChosenFiniteProducts.lean | import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
deprecated_module (since := "2025-05-15")
|
HasOuterApproxClosed.lean | /-
Copyright (c) 2022 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
import Mathlib.MeasureTheory.Integral.BoundedContinuousFunction
import Mathlib.Topology.MetricSpace.ThickenedIndicator
/-!
# Spaces where indicators of closed sets have ... |
Prod.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, Alexander Bentkamp
-/
import Mathlib.LinearAlgebra.Prod
import Mathlib.LinearAlgebra.Basis.Defs
import Mathlib.LinearAlgebra.Finsupp.SumProd
import Math... |
polydiv.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 choice.
From mathcomp Require Import fintype bigop ssralg poly.
(**********************... |
monoid.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq.
From mathcomp Require Import bigop fintype finfun.
(******************************************************************************)
(* Group-like structures ... |
extremal.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... |
fingroup.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 div path... |
ClosedSubgroup.lean | /-
Copyright (c) 2024 Nailin Guan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nailin Guan
-/
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.GroupTheory.Index
import Mathlib.Topology.Algebra.Group.Basic
/-!
# Closed subgroups of a topological group
Th... |
test_intro_rw.v | From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Lemma test_dup1 : forall n : nat, odd n.
Proof. move=> /[dup] m n; suff: odd n by []. Abort.
Lemma test_dup2 : let n := 1 in False.
Proof. move=> /[dup] m n; have : m = n :=... |
Normalize.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.Normalize
import Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes
/-!
# Normalization of 2-morphisms in bicategories
This... |
Hom.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Analysis.Normed.Group.Int
import Mathlib.Analysis.Normed.Group.Subgroup
import Mathlib.Analysis.Normed.Group.Uniform
/-!
# Normed groups homomorphisms... |
simp_confluence.lean | import Mathlib
namespace Set
open Function
variable {α β : Type*}
/-- Without `subset_range_of_surjective`, `image_subset_iff` and `image_preimage_eq` create a simp
confluence issue. -/
example {f : α → β} (s t : Set β) (h : Surjective f) :
f '' (f ⁻¹' s) ⊆ t ↔ f '' (f ⁻¹' s) ⊆ t := by
conv =>
congr
... |
Ineq.lean | /-
Copyright (c) 2020 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import Mathlib.Lean.Expr.Basic
/-!
# `Ineq` datatype
This file contains an enum `Ineq` (whose constructors are `eq`, `le`, `lt`), and operations
involving it. The... |
Ker.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.Order.Filter.Map
/-!
# Kernel of a filter
In this file we define the *kernel* `Filter.ker f` of a filter `f`
to be the intersection of all its sets.
We ... |
UpperLower.lean | /-
Copyright (c) 2022 Yaël Dillies, Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Kexing Ying
-/
import Mathlib.Analysis.Normed.Order.UpperLower
import Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace
import Mathlib.Topology.Order.Dense... |
Defs.lean | /-
Copyright (c) 2021 Damiano Testa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa
-/
import Mathlib.Algebra.Notation.Defs
import Mathlib.Logic.Function.Defs
/-!
# Regular elements
We introduce left-regular, right-regular and regular elements, along wi... |
Sigma.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.Data.Finset.Sigma
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Product and sums indexed by finite sets in sigma types.
-/
variable {... |
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... |
InvariantBasisNumber.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.Algebra.Module.Projective
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.Matrix.SemiringInverse
import Mathlib.LinearAlgebra.Invari... |
Basic.lean | /-
Copyright (c) 2019 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.Algebra.Group.Submonoid.Operations
import Mathlib.Data.Setoid.Basic
import Mathlib.GroupTheory.Congruence.Hom
/-!
# Congruence relations
This f... |
Induced.lean | /-
Copyright (c) 2025 Amelia Livingston. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Amelia Livingston
-/
import Mathlib.RepresentationTheory.Coinvariants
/-!
# Induced representations
Given a commutative ring `k`, a group homomorphism `φ : G →* H`, and a `k`-line... |
Basic.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.Localization.Resolution
import Mathlib.CategoryTheory.Localization.Opposite
import Mathlib.CategoryTheory.GuitartExact.Opposite
/-!
# Derivabilit... |
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... |
burnside_app.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tupl... |
IntegrallyClosed.lean | /-
Copyright (c) 2024 Yongle Hu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yongle Hu
-/
import Mathlib.RingTheory.IntegralClosure.IntegrallyClosed
import Mathlib.RingTheory.LocalProperties.Basic
import Mathlib.RingTheory.Spectrum.Maximal.Localization
/-!
# `IsInt... |
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... |
AffineMap.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Algebra.Order.Group.Pointwise.Interval
import Mathlib.Algebra.Order.Module.Defs
import Mathlib.LinearAlgebra.BilinearMap
import Mathlib.LinearAlgebra.Pi
im... |
Generalized.lean | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Polynomial.Content
import Mathlib.RingTheory.Ideal.Quotient.Defs
deprecated_module "Aut... |
Divisibility.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.IsPrimePow
import Mathlib.SetTheory.Cardinal.Arithmetic
import Mathlib.Tactic.WLOG
/-!
# Cardinal Divisibility
We show basic results about di... |
Field.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.RingTheory.SimpleRing.Basic
import Mathlib.Algebra.Ring.Subring.Basic
import Mathlib.Algebra.Field.Equiv
/-!
# Simple ring and fields
## Main results
- ... |
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
-/
import Mathlib.CategoryTheory.Sites.Sheaf
import Mathlib.Topology.Category.CompHaus.EffectiveEpi
/-!
# Condensed Objects
This file defines the category of condensed objec... |
BigOperators.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.BigOperators.Group.Finset.Piecewise
import Mathlib.Algebra.BigOperators.Group.Finset.Sigma
import Mathlib.Algebra.BigOperators.Option
import Ma... |
List.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.Logic.Denumerable
/-!
# Equivalences involving `List`-like types
This file defines some additional constructive equivalences using `Encodable` and th... |
CanonicalTensor.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Canonical tensors in real inner product spaces
Given an `InnerProductSpace ℝ E`, this file defines two canonic... |
Continuity.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel,
Rémy Degenne, David Loeffler
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
/-!
# Continu... |
Basic.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Chris Hughes, Mario Carneiro
-/
import Mathlib.RingTheory.Jacobson.Ideal
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Defs
import Mathlib.RingTheory.Spectrum.Maximal.Defs
/-... |
WithAlgebraicStructures.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic
import Mathlib.Algebra.Category.ModuleCat.Basic
import Mathlib.Tactic.CategoryTheory.Elementwise
/-!
# Colimi... |
FullSubcategory.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.Limits.Creates
import Mathlib.CategoryTheory.ObjectProperty.ClosedUnderIsomorphisms
/-!
# Limits in full subcategories
We introduce the ... |
NeLocus.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.Finsupp
/-!
# Locus of unequal values of finitely supported functions
Let `α N` be two Types, assume that `N` has a `0` and let `f g : α ... |
Basis.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.LinearAlgebra.AffineSpace.Centroid
import Mathlib.LinearAlgebra.AffineSpace.Independent
import Mathlib.LinearAlgebra.AffineSpace.Pointwise
import Mathlib.Lin... |
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... |
ExtendFrom.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.ExtendFrom
import Mathlib.Topology.Order.DenselyOrdered
/-!
# Lemmas about `extendFrom` in an order topology... |
ring_quotient.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat.
From mathcomp Require Import seq ssralg generic_q... |
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.
|
CDFToKernel.lean | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.AEEqOfIntegral
import Mathlib.Probability.Kernel.Composition.CompProd
import Mathlib.Probability.Kernel.Disintegration.MeasurableSti... |
Countable.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
-/
import Mathlib.MeasureTheory.Integral.Lebesgue.Map
import Mathlib.MeasureTheory.Integral.Lebesgue.Markov
import Mathlib.MeasureTheory.Measure.Count
/... |
MazurUlam.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.Topology.Instances.RealVectorSpace
import Mathlib.Analysis.Normed.Affine.Isometry
/-!
# Mazur-Ulam Theorem
Mazur-Ulam theorem states that an isomet... |
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