filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
SequentialLimit.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.Functor.OfSequence
import Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective
import Mathlib.CategoryTheory.Sites.EpiMono
import... |
Floor.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.Order.Floor.Defs
import Mathlib.Algebra.Order.Nonneg.Basic
/-!
# Nonnegative elements are archimedean
This file defines instances and pro... |
RestrictedProduct.lean | import Mathlib.Topology.Algebra.RestrictedProduct.Basic
import Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace
deprecated_module (since := "2025-06-11")
|
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... |
Squarefree.lean | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Algebra.Squarefree.Basic
import Mathlib.Data.Nat.Factorization.PrimePow
import Mathlib.RingTheory... |
ArchimedeanDensely.lean | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Order.Group.Units
import Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder
import Mathlib.Data.Int.Interval
import Mathlib.GroupTheory.Archimed... |
Submodule.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Module.Submodule.Invariant
import Mathlib.RepresentationTheory.Basic
/-!
# Invariant submodules of a group representation
-/
variable {k G V : Typ... |
FixingSubgroup.lean | /-
Copyright (c) 2022 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir
-/
import Mathlib.Algebra.Group.Subgroup.Lattice
import Mathlib.GroupTheory.GroupAction.FixedPoints
/-!
# Fixing submonoid, fixing subgroup of an action
... |
sesquilinear.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup.
From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector.
(************************************************... |
BifunctorFlip.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.TotalComplexSymmetry
/-!
# Action of the flip of a bifunctor on homological complexes
Given `K₁ : Ho... |
test_order_conv.v | From mathcomp Require Import all_boot all_order.
Import Order.Theory.
Section dual_of_dual.
Context (disp : Order.disp_t).
Let eq_dual_dual_preorderType (T : preorderType disp) :
Order.Preorder.on T = Order.Preorder.on T^d^d := erefl.
Let eq_dual_dual_porderType (T : porderType disp) :
Order.POrder.on T = Order.... |
WeakDual.lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Yury Kudryashov
-/
import Mathlib.Analysis.Normed.Module.Dual
import Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness
import Mathlib.Topology.Algebra.Module.WeakDual
... |
Graph.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, David Loeffler
-/
import Mathlib.Algebra.Group.Subgroup.Ker
/-!
# Vertical line test for group homs
This file proves the vertical line test for monoid homomorphisms/isomo... |
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.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.RingTheory.Kaehler.Basic
/-!
# The differentials of a morphis... |
DiscreteValuationRing.lean | /-
Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Heather Macbeth, Johan Commelin
-/
import Mathlib.RingTheory.WittVector.Domain
import Mathlib.RingTheory.WittVector.MulCoeff
import Mathlib.RingTheory.DiscreteValuati... |
Weight.lean | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina
-/
import Mathlib.Combinatorics.Quiver.Path
import Mathlib.Algebra.Order.Ring.Defs
/-!
# Path weights in a Quiver
This file defines the weight of a path in a quiv... |
SymmDiff.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, Minchao Wu, Mario Carneiro
-/
import Mathlib.Data.Finset.Image
import Mathlib.Data.Set.SymmDiff
/-!
# Symmetric difference of finite sets
Thi... |
Circle.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.Analysis.Complex.Circle
import Mathlib.Analysis.SpecialFunctions.Complex.Log
/-!
# Maps on the unit circle
In this file we prove some basic lemmas ... |
Basic.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.Data.Multiset.ZeroCons
/-!
# Basic results on multisets
-/
-- No algebra should be required
assert_not_exists Monoid
universe v
open List S... |
Archimedean.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.GroupTheory.Archimedean
import Mathlib.Topology.Algebra.Order.Group
import Mathlib.Algebra.Group.Subgroup.ZPowers.Basic
import Mathlib.Topology.Order... |
all_algebra.v | (* N.B. interval_inference is not exported here.
To enjoys the automation it provides,
you need to explictly "Import interval_inference". *)
From mathcomp Require Export ssralg.
From mathcomp Require Export ssrnum.
From mathcomp Require Export finalg.
From mathcomp Require Export countalg.
From mathcomp Require Export... |
UnivLE.lean | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Logic.Small.Defs
/-!
# UnivLE
A proposition expressing a universe inequality. `UnivLE.{u, v}` expresses that `u ≤ v`,
in the form `∀ α : Type u, Small.{v... |
Indicator.lean | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic
/-!
# Conditional expectation of indicator functions
This file proves some results about the conditi... |
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.
... |
Defs.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.LinearAlgebra.Determinant
/-!
# Norm for (finite) ring extensions
Suppose we have an `R`-algebra `S` with a finite basis. For each `s : S`,
the determinant... |
LinearFunctor.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.Monoidal.Action.Basic
/-! # Functors that are linear with respect to an action
Given a monoidal category `C` acting on the left or on th... |
PoincareConjecture.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.AlgebraicTopology.FundamentalGroupoid.SimplyConnected
import Mathlib.Geometry.Manifold.Diffeomorph
import Mathlib.Geometry.Manifold.Instances.Sphere
import Mathl... |
ZetaValues.lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.NumberTheory.BernoulliPolynomials
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
import Mathlib.Analysis.Calculus.Deriv.Polynomial
import... |
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... |
StringDiagram.lean | import Mathlib.Tactic.Widget.StringDiagram
import ProofWidgets.Component.Panel.SelectionPanel
/-! ## Example use of string diagram widgets -/
open ProofWidgets Mathlib.Tactic.Widget
section MonoidalCategory
open CategoryTheory
open scoped MonoidalCategory
universe v u
variable {C : Type u} [Category.{v} C] [Monoi... |
Degree.lean | /-
Copyright (c) 2024 David Kurniadi Angdinata. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Kurniadi Angdinata
-/
import Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic
import Mathlib.Tactic.ComputeDegree
/-!
# Division polynomials of Weierst... |
Polynomial.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.LinearAlgebra.Charpoly.BaseChange
import Mathlib.LinearAlgebra.Eigenspace.Zero
import Mathlib.RingTheory.AdjoinRoot
import Mathlib.RingTheory.LocalRing.Resid... |
Prod.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.MeasureTheory.Group.Measure
import Mathlib.MeasureTheory.Measure.Prod
/-!
# Measure theory in the product of groups
In this file we show propertie... |
AssertImported.lean | import Mathlib
/-
This file checks that every declaration and import that have been flagged with
`assert_not_exists` or `assert_not_imported` is present in the environment once
all of `Mathlib` is available.
-/
#check_assertions!
|
Basic.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.Analysis.BoxIntegral.Partition.Filter
import Mathlib.Analysis.BoxIntegral.Partition.Measure
import Mathlib.Analysis.Oscillation
import Mathlib.Data.B... |
instance_diamonds.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.EuclideanDomain.Field
import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.GroupWithZero.Action.Prod
import Mathlib.Algebra.GroupWithZero.Action.... |
Preadditive.lean | /-
Copyright (c) 2023 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Quotient
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
/-!
# The quotient category is preadditive
If an equivalence relation `r : Ho... |
inertia.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path.
From mathcomp Require Import choice fintype div... |
binomial.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 div fintype tuple ... |
says.lean | import Mathlib.Tactic.Says
import Aesop
-- removing changes to the `simp` set after this test was created
attribute [-simp] Nat.add_left_cancel_iff Nat.add_right_cancel_iff
set_option autoImplicit true
/--
info: Try this: (show_term exact 37) says exact 37
-/
#guard_msgs in
example : Nat := by
(show_term exact 37) ... |
CategoryWithFibrations.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.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
import Mathlib.AlgebraicTopology.SimplicialSet.Boundary
import Mathlib.AlgebraicTopology.SimplicialSet.H... |
Division.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Algebra.Group.Hom.End
import Mathlib.Algebra.MonoidAlgebra.Defs
/-!
# Division of `AddMonoidAlgebra` by monomials
This file is most important for when `G =... |
gseries.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import fintype bigop finset fingroup morphism.
From mathcomp... |
Pi.lean | /-
Copyright (c) 2022 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Alex J. Best
-/
import Mathlib.LinearAlgebra.Pi
import Mathlib.LinearAlgebra.Quotient.Basic
/-!
# Submodule quotients and direct sums
This file contains some results on the... |
Small.lean | /-
Copyright (c) 2023 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.Filtered.Basic
/-!
# A functor from a small category to a filtered category factors throug... |
FunctorToTypes.lean | /-
Copyright (c) 2024 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
import Mathlib.CategoryTheory.Limits.Types.Colimits
/-!
# Concrete description of (co)limits in functor cate... |
Option.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.Fintype.EquivFin
import Mathlib.Data.Finset.Option
/-!
# fintype instances for option
-/
assert_not_exists MonoidWithZero MulAction
open Functi... |
Set.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.Data.Set.Image
/-!
# Booleans and set operations
This file contains two trivial lemmas about `Bool`, `Set.univ`, and `Set.range`.
-/
open Set
na... |
Lemmas.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.Fintype.Card
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.Nat.Prime.Basic
import Mathlib.Data.PNat.Basic
import Mathlib.Data.Set.Lat... |
seq.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat.
(******************************************************... |
MultiplePrimitivity.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.GroupTheory.GroupAction.MultipleTransitivity
import Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
/-! # Multiply prepri... |
Basic.lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Kim Morrison
-/
import Mathlib.CategoryTheory.Adjunction.FullyFaithful
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Constructions.... |
Lex.lean | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
import Mathlib.Algebra.Group.Prod
import Mathlib.Algebra.Order.Hom.Monoid
import Mathlib.Data.Prod.Lex
import Mathlib.Order.Prod.Lex.Hom
/-!
# Order homomorphisms ... |
algnum.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... |
Basic.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Robin Carlier
-/
import Mathlib.CategoryTheory.Equivalence
/-!
# Binary disjoint unions of categories
We define the category instance on `C ⊕ D` when `C` and `D` are cate... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Order.Bounds.Defs
import Mathlib.Order.Directed
import Mathlib.Order.BoundedOrder.Monotone
import Mathlib.Order.Interval.Set.Basic
/-... |
Closed.lean | /-
Copyright (c) 2025 Robin Carlier. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robin Carlier
-/
import Mathlib.CategoryTheory.Monoidal.DayConvolution
import Mathlib.CategoryTheory.Closed.Monoidal
import Mathlib.CategoryTheory.Limits.Shapes.End
/-! # Internal homs... |
WithZero.lean | /-
Copyright (c) 2024 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.Algebra.Order.GroupWithZero.Canonical
import Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic
/-!
# Covariant instances on `WithZero`
Adding a zero ... |
mxred.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 div.
From mathcomp Require Import choice fintype finfun bigop fingroup perm order.
From ... |
CircleAverage.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.MeasureTheory.Integral.CircleIntegral
import Mathlib.MeasureTheory.Integral.IntervalAverage
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Peri... |
ssrfun.v | From mathcomp Require Import ssreflect.
From Corelib Require Export ssrfun.
From mathcomp Require Export ssrnotations.
#[export] Set Warnings "-overwriting-delimiting-key".
(* remove above line when requiring Rocq >= 9.0 *)
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
(***********... |
Basic.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.Data.Fintype.Parity
import Mathlib.NumberTheory.LegendreSymbol.ZModChar
import Mathlib.FieldTheory.Finite.Basic
/-!
# Quadratic characters of finite fie... |
tactic_timeout.lean | import Mathlib.Tactic.Linarith
/-!
# Test that tactics respond to a cancellation request
-/
variable {α}
open Lean Elab Tactic
/-! versions of try/catch that catch `interrupted` too -/
section catch_interrupted
attribute [-instance]
Lean.instMonadExceptOfExceptionCoreM Lean.Elab.Tactic.instMonadExceptExceptionT... |
Basic.lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Star.Pointwise
import Mathlib.RingTheory.Ideal.Maps
import Mathlib.RingTheory.Ideal.Nonunits
impo... |
Covariance.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Etienne Marion
-/
import Mathlib.Probability.Independence.Integration
/-!
# Covariance
We define the covariance of two real-valued random variables.
## Main definitions
... |
fraction.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq.
From mathcomp Require Import ssrAC choice tuple ... |
Gluing.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.CategoryTheory.GlueData
import Mathlib.Topology.Category.TopCat.Limits.Pullbacks
import Mathlib.Topology.Category.TopCat.Opens
import Mathlib.Tactic.Generali... |
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... |
Topology.lean | /-
Copyright (c) 2025 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Christian Merten
-/
import Mathlib.Algebra.Category.Ring.Colimits
import Mathlib.Algebra.Category.Ring.Constructions
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathl... |
Class.lean | /-
Copyright (c) 2025 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Group.Subgroup.Lattice
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Algebra.Ord... |
observe.lean | import Mathlib.Tactic.Observe
import Mathlib.Tactic.AdaptationNote
set_option linter.unusedVariables false
/-- info: Try this: have h : x + y = y + x := Nat.add_comm x y -/
#guard_msgs in
example (x y : Nat) : True := by
observe? h : x + y = y + x
guard_hyp h : x + y = y + x
trivial
|
Invertible.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.Algebra.GroupWithZero.Invertible
import Mathlib.Algebra.Ring.Defs
/-!
# Theorems about invertible elements in rings
-/
universe u
variable {R : Type u}
/... |
Multiset.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Order.Interval.Finset.Basic
/-!
# Intervals as multisets
This file defines intervals as multisets.
## Main declarations
In a `LocallyFiniteOrder`,
* `M... |
Basic.lean | /-
Copyright (c) 2022 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
import Mathlib.Algebra.Module.ZLattice.Basic
import Mathlib.Analysis.InnerProductSpace.ProdL2
import Mathlib.MeasureTheory.Measure.Haar.Unique
import Mathlib.NumberTheo... |
Minimal.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Existence of minimizers (Hilbert p... |
Multiset.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.Group.Hom.Defs
import Mathlib.Algebra.Group.Nat.Defs
import Mathlib.Algebra.Order.Monoid.Unbundled.ExistsOfLE
import Mathlib.Algebra.Ord... |
fingraph.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat.
From mathcomp Require Import seq path fintype.
(******************************************... |
interval_inference.v | (* mathcomp analysis (c) 2017 Inria and AIST. License: CeCILL-C. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype choice.
From mathcomp Require Import order ssralg ssrnum ssrint interval.
(**md********************************************************... |
Quaternion.lean | import Mathlib.Algebra.Quaternion
import Mathlib.Data.Real.Basic
import Mathlib.NumberTheory.Zsqrtd.GaussianInt
open Quaternion
/--
info: { re := 0, imI := 0, imJ := 0, imK := 0 }
-/
#guard_msgs in
#eval (0 : ℍ[ℚ])
/--
info: { re := 1, imI := 0, imJ := 0, imK := 0 }
-/
#guard_msgs in
#eval (1 : ℍ[ℚ])
/--
info: { re ... |
CommGrp_.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.Monoidal.Grp_
import Mathlib.CategoryTheory.Monoidal.CommMon_
/-!
# The category of commutative groups in a cartesian monoidal category
-... |
DistribChar.lean | /-
Copyright (c) 2024 Andrew Yang, Yaël Dillies, Javier López-Contreras. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yaël Dillies, Javier López-Contreras
-/
import Mathlib.MeasureTheory.Measure.Haar.Unique
/-!
# The distributive character of Haar measu... |
AbsoluteGaloisGroup.lean | /-
Copyright (c) 2023 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
import Mathlib.FieldTheory.KrullTopology
import Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure
import Mathlib.Topology.Algebra.Group... |
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 ... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
Limits.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Abelian.FunctorCategory
import Mathlib.CategoryTheory.Abelian.Transfer
import Mathlib.CategoryTheory.Linear.LinearFunctor
import Mathlib.Cat... |
action.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype.
From mathcomp Require Import ssrnat div seq prime fintype bigop finset.
From mathcomp... |
action.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype.
From mathcomp Require Import ssrnat div seq prime fintype bigop finset.
From mathcomp... |
LocallyBijective.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.Sites.LocallySurjective
import Mathlib.CategoryTheory.Sites.Localization
/-!
# Locally bijective morphisms of presheaves
Let `C` a be category e... |
Hom.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Antoine Chambert-Loir
-/
import Mathlib.Algebra.Group.Hom.CompTypeclasses
import Mathlib.Algebra.Module.Defs
import Mathlib.Algebra.Notation.Prod
import Mathlib.Algebra.Regular.... |
LiftLets.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.Tactic.Basic
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module "The lift_lets tactic was moved to Lean core; \
you can probably just remove ... |
Semisimple.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Matrix
import Mathlib.Algebra.Lie.Semisimple.Lemmas
import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic
import Mathlib.RingTheory.Fini... |
congr.lean | import Mathlib.Tactic.CongrExclamation
import Mathlib.Algebra.BigOperators.Ring.List
import Mathlib.Algebra.Group.Basic
import Mathlib.Data.Subtype
private axiom test_sorry : ∀ {α}, α
set_option autoImplicit true
-- Useful for debugging the generated congruence theorems
--set_option trace.Meta.CongrTheorems true
the... |
AdmissibleCardPowDegree.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.Algebra.Polynomial.Degree.CardPowDegree
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
imp... |
Defs.lean | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov
-/
import Mathlib.Analysis.Asymptotics.TVS
/-!
# The Fréchet derivative: definition
Let `E` and `F` be normed spaces, `f : E → F`, an... |
SmallShiftedHom.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.SmallHom
import Mathlib.CategoryTheory.Shift.ShiftedHom
import Mathlib.CategoryTheory.Shift.Localization
/-!
# Shrinking morphisms i... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-/
import Mathlib.Algebra.Group.Subgroup.Pointwise
import Mathlib.Algebra.Group.Submonoid.Units
import Mathlib.Algebra.Group.Submonoid.Mu... |
delabLinearIndependent.lean | import Mathlib.LinearAlgebra.LinearIndependent.Defs
set_option linter.style.setOption false
set_option pp.unicode.fun true
set_option linter.style.commandStart false
variable {K V : Type*} [DivisionRing K] [AddCommGroup V] [Module K V] {s : Set V} {x : V}
variable (h : LinearIndependent K (fun b => b : s → V)) in
/-... |
EnvExtension.lean | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import Mathlib.Init
import Lean.ScopedEnvExtension
/-!
# Helper function for environment extensions and attributes.
-/
open Lean
instance {σ : Type} [Inhabited... |
Equiv.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.Opposite
import Mathlib.Algebra.GroupWithZero.Equiv
import Mathlib.Algebra.GroupWithZero.InjSurj
im... |
Prod.lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Patrick Massot, Eric Wieser
-/
import Mathlib.Algebra.Group.Action.Prod
import Mathlib.Algebra.GroupWithZero.Action.End
/-!
# Prod instances for multiplicative actions with ... |
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