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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 ...