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Defs.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes HΓΆlzl, Mario Carneiro, Anne Baanen, FrΓ©dΓ©ric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.LinearMap.Defs /-! # (Semi)linear equiva...
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. (*********************...
Behrend.lean
/- Copyright (c) 2022 YaΓ«l Dillies, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies, Bhavik Mehta -/ import Mathlib.Analysis.InnerProductSpace.Convex import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.Combinatorics.Additive.AP.Three...
CompactlyCoherentSpace.lean
/- Copyright (c) 2025 Floris van Doorn and Hannah Scholz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Hannah Scholz -/ import Mathlib.Topology.Coherent import Mathlib.Topology.Compactness.Compact /-! # Compactly coherent spaces and the k-ificatio...
Equiv.lean
/- Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Group.Equiv.Basic import Mathlib.Algebra.Group.Units.Hom /-! # Multiplicative and additive equivalence acting ...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
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 :=...
Pullbacks.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.Limits.FunctorCategory.Basic import Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback /-! # Pullbacks in functor categories We p...
ReflectsIso.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.ConcreteCategory.Basic import Mathlib.CategoryTheory.Functor.ReflectsIso.Basic /-! A `forgetβ‚‚ C D` forgetful functor between concrete categ...
Prufer.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Dynamics.FixedPoints.Basic /-! # Results about pointwise operations on sets with iteration. -/ ope...
Basic.lean
/- Copyright (c) 2025 Yunzhou Xie. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yunzhou Xie, Jujian Zhang -/ import Mathlib.Algebra.Azumaya.Defs import Mathlib.LinearAlgebra.Matrix.ToLin import Mathlib.RingTheory.Finiteness.Basic import Mathlib.GroupTheory.GroupActio...
Equalizers.lean
/- Copyright (c) 2020 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer import Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer import Mathlib.CategoryTheory.Limits.Preserves.Bas...
Four.lean
/- Copyright (c) 2020 Paul van Wamelen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul van Wamelen -/ import Mathlib.Data.Nat.Factors import Mathlib.NumberTheory.FLT.Basic import Mathlib.NumberTheory.PythagoreanTriples import Mathlib.RingTheory.Coprime.Lemmas impo...
Measure.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Algebra.Group.Pointwise.Set.Card import Mathlib.MeasureTheory.Group.Action import Mathlib.MeasureTheory.Measure.Prod import Mathlib.Topology.Algebr...
UniformConvergence.lean
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Topology.Algebra.UniformMulAction import Mathlib.Algebra.Module.Pi import Mathlib.Topology.UniformSpace.UniformConvergenceTopology /-! # Algebraic...
sylow.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 div. From mathcomp Require Import fintype prime bigop finset fingroup morphism. From mat...
Colimits.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Sophie Morel -/ import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.Algebra.Group.Shrink import Mathlib.CategoryTheory.ConcreteCategory.Elementwise import Mathli...
ULift.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Jannis Limperg -/ import Mathlib.Init /-! # Monadic instances for `ULift` and `PLift` In this file we define `Monad` and `IsLawfulMonad` instances on `PLift` and `ULift`....
KanComplex.lean
/- Copyright (c) 2023 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, JoΓ«l Riou -/ import Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant import Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations import Mathlib.AlgebraicTo...
Strong.lean
/- Copyright (c) 2023 YaΓ«l Dillies, Chenyi Li. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chenyi Li, Ziyu Wang, YaΓ«l Dillies -/ import Mathlib.Analysis.Convex.Function import Mathlib.Analysis.InnerProductSpace.Basic /-! # Uniformly and strongly convex functions I...
OneDim.lean
/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.MeasureTheory.Covering.DensityTheorem import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar /-! # Covering theorems for Lebesgue measure in one d...
separable.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...
CMField.lean
/- Copyright (c) 2025 X. Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Units.DirichletTheorem /-! # CM-extension of number fields...
Lattice.lean
/- Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes HΓΆlzl -/ import Mathlib.Order.BoundedOrder.Basic import Mathlib.Order.Lattice /-! # Bounded lattices This file defines top and bottom elements (greatest and least elements) ...
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...
Defs.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Neil Strickland -/ import Mathlib.Data.Int.Order.Basic import Mathlib.Data.Nat.Basic import Mathlib.Data.PNat.Notation import Mathlib.Order.Basic import Mathlib....
Nonempty.lean
/- Copyright (c) 2024 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.CategoryTheory.SmallObject.Iteration.Basic import Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc import Mathlib.CategoryTheory.SmallObject.Iteration.F...
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 :=...
CommandStart.lean
import Aesop.Frontend.Attribute import Mathlib.Tactic.Linter.CommandStart import Mathlib.Tactic.Lemma set_option linter.style.commandStart true /-- warning: missing space in the source This part of the code 'example: True' should be written as 'example : True' Note: This linter can be disabled with `set_option...
FreeGroupoid.lean
/- Copyright (c) 2022 RΓ©mi Bottinelli. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: RΓ©mi Bottinelli -/ import Mathlib.CategoryTheory.Groupoid import Mathlib.CategoryTheory.PathCategory.Basic /-! # Free groupoid on a quiver This file defines the free groupoid on a q...
UniversallyInjective.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.PullbackCarrier import Mathlib.Topology.LocalAtTarget /-! # Universally injective morphism A morphism of schemes `f : X ⟢ Y` is universal...
SpecificAsymptotics.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent import Mathlib.Analysis.SpecialFunctions.Pow.Continuity /-! # A collection of specific asymptotic result...
Mem.lean
/- Copyright (c) 2022 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Devon Tuma -/ import Mathlib.Data.Vector.Basic /-! # Theorems about membership of elements in vectors This file contains theorems for membership in a `v.toList` for a vector `v`. Having ...
Exact.lean
/- Copyright (c) 2023 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.Algebra.Homology.ShortComplex.PreservesHomology import Mathlib.Algebra.Homology.ShortComplex.Abelian import Mathlib.Algebra.Homology.ShortComplex.QuasiIso import...
Degeneracies.lean
/- Copyright (c) 2022 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.AlgebraicTopology.DoldKan.Decomposition import Mathlib.Tactic.FinCases /-! # Behaviour of P_infty with respect to degeneracies For any `X : SimplicialObject C...
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...
Nat.lean
/- Copyright (c) 2014 Floris van Doorn (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Leonardo de Moura, Jeremy Avigad, Mario Carneiro -/ import Mathlib.Data.Nat.Find import Mathlib.Order.BoundedOrder.Basic import Mathl...
gfunctor.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype. From mathcomp Require Import bigop finset fingroup morphism automorphism. From math...
Images.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Reid Barton -/ import Mathlib.CategoryTheory.Limits.Types.Limits import Mathlib.CategoryTheory.Limits.Shapes.Images /-! # Images in the category of types In this file, it...
Four.lean
/- Copyright (c) 2020 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel, JoΓ«l Riou -/ import Mathlib.Algebra.Homology.ExactSequence import Mathlib.CategoryTheory.Abelian.Refinements /-! # The four and five lemmas Consider the following commu...
order.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...
AddCircle.lean
/- Copyright (c) 2022 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Dynamics.FixedPoints.Prufer import Mathlib.Dynamics.Ergodic.Ergodic import Mathlib.MeasureTheory.Covering.DensityTheore...
RCLike.lean
/- Copyright (c) 2023 Xavier GΓ©nΓ©reux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier GΓ©nΓ©reux, Patrick Massot -/ import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Analysis.RCLike.Basic /-! # A collection of specific limit computations for `RCLike` -...
Continuous.lean
/- Copyright (c) 2019 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, SΓ©bastien GouΓ«zel, FrΓ©dΓ©ric Dupuis -/ import Mathlib.Analysis.InnerProductSpace.Basic import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps /-! # Continuity of inne...
Cardinality.lean
/- Copyright (c) 2019 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.Group.Pointwise.Interval import Mathlib.Analysis.SpecificLimits.Basic import Mathlib.Data.Rat.Cardinal import Mathlib.SetTheory.Cardi...
PiLex.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Order.WellFounded import Mathlib.Tactic.Common /-! # Lexicographic order on Pi types This file defines the lexicographic order for Pi types. `a` is less ...
GromovHausdorff.lean
/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.Logic.Encodable.Pi import Mathlib.SetTheory.Cardinal.Basic import Mathlib.Topology.MetricSpace.Closeds import Mathlib.Topology.MetricSpace.Comple...
Prod.lean
/- Copyright (c) 2018 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.Algebra.NoZeroSMulDivisors.Defs import Mathlib.Algebra.Notation.Prod /-! # Prod instances for NoZeroSMulDivisors This file defines a NoZeroSMulDivisors ins...
cyclic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import div fintype bigo...
Comparison.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Coherent.Basic import Mathlib.CategoryTheory.EffectiveEpi.Comp import Mathlib.CategoryTheory.EffectiveEpi.Extensive /-! # Con...
Vandermonde.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.Algebra.Polynomial.Coeff import Mathlib.Data.Nat.Choose.Basic /-! # Vandermonde's identity In this file we prove Vandermonde's identity (`Nat.add_ch...
PeakFunction.lean
/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.MeasureTheory.Integral.IntegralEqImproper /-! # Integrals against peak functions A sequence of peak functions is a sequence of functions with a...
Functor.lean
/- Copyright (c) 2021 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies, Kim Morrison -/ import Mathlib.Data.Finset.Lattice.Union import Mathlib.Data.Finset.NAry import Mathlib.Data.Multiset.Functor /-! # Functoriality of `Finset` This file de...
CauSeqFilter.lean
/- Copyright (c) 2018 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, SΓ©bastien GouΓ«zel -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Topology.MetricSpace.Cauchy /-! # Completeness in terms of `Cauchy` filters vs `isCauS...
NotNormal.lean
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Data.Real.Cardinality import Mathlib.Topology.TietzeExtension /-! # Not normal topological spaces In this file we prove (see `IsClosed.not_normal_of...
Defs.lean
/- Copyright (c) 2016 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura -/ import Mathlib.Init import Batteries.Util.ExtendedBinder import Lean.Elab.Term /-! # Sets This file sets up the theory of sets whose elements have a given...
Colimit.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.Comma.Presheaf.Basic import Mathlib.CategoryTheory.Limits.Preserves.Yoneda import Mathlib.CategoryTheory.Limits.Over /-! # Relative Yoned...
GradedMonoid.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.BigOperators.Group.List.Lemmas import Mathlib.Algebra.Group.Action.Hom import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Data.List.FinRange ...
Rotation.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Heather Macbeth -/ import Mathlib.Analysis.SpecialFunctions.Complex.Circle import Mathlib.Geometry.Euclidean.Angle.Oriented.Basic /-! # Rotations by oriented angles. This...
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...
ZeroObjects.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.CategoryTheory.Limits.Shapes.ZeroMorphisms import Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts /-! # Limits involving zero objects Binary p...
FullyFaithful.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.NatIso import Mathlib.Logic.Equiv.Defs /-! # Full and faithful functors We define typeclasses `Full` and `Faithful`, decorating functors. ...
matrix.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq choice. From mathcomp Require Import fintype finfun f...
ContinuousLinearMap.lean
/- Copyright (c) 2020 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot -/ import Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic import Mathlib.Topology.Algebra.Module.FiniteDim...
fin_cases.lean
import Mathlib.Tactic.FinCases import Mathlib.Tactic.NormNum.Basic import Mathlib.Order.Interval.Finset.Nat example {x : Nat} (h : x ∈ [0, 2, 37]) : x ≀ 57 := by fin_cases h repeat decide example {x : Nat} (h : x ∈ [0, 2, 37]) : x = 0 ∨ x = 2 ∨ x = 37 := by fin_cases h repeat simp example {x : Nat} (h : x ∈ ...
Sampleable.lean
/- Copyright (c) 2022 Henrik BΓΆving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik BΓΆving, Simon Hudon -/ import Batteries.Data.Rat.Basic import Mathlib.Data.Int.Order.Basic import Mathlib.Data.List.Monad import Mathlib.Data.PNat.Defs import Plausible.Sampleabl...
Pi.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.Pi import Mathlib.LinearAlgebra.Multilinear.Basic /-! # Interactions between (dependent) functions and multilinear maps ## Main definitions ...
numdomain.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...
Elementwise.lean
import Mathlib.Tactic.CategoryTheory.Elementwise import Mathlib.Algebra.Category.MonCat.Basic set_option autoImplicit true namespace ElementwiseTest open CategoryTheory namespace HasForget attribute [simp] Iso.hom_inv_id Iso.inv_hom_id IsIso.hom_inv_id IsIso.inv_hom_id attribute [local instance] HasForget.instFunL...
Indicator.lean
/- Copyright (c) 2020 Zhouhang Zhou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Notation.Indicator /-! # Indicato...
ModularCharacter.lean
/- Copyright (c) 2025 Noam Atar. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Noam Atar -/ import Mathlib.MeasureTheory.Function.LocallyIntegrable import Mathlib.MeasureTheory.Group.Integral import Mathlib.MeasureTheory.Group.Measure import Mathlib.Topology.Metrizabl...
PartialAdjoint.lean
/- Copyright (c) 2024 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.CategoryTheory.Adjunction.Basic import Mathlib.CategoryTheory.Limits.HasLimits import Mathlib.CategoryTheory.Yoneda /-! # Domain of definition of the partial l...
Open.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Cover.MorphismProperty /-! # Open covers of schemes This file provides the basic API for open covers of schemes. ## Main definition - `A...
Connected.lean
/- Copyright (c) 2021 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Combinatorics.SimpleGraph.Connectivity.WalkDecomp import Mathlib.Combinatorics.SimpleGraph.Paths import Mathlib.Combinatorics.SimpleGraph.Subgraph /-! ## Ma...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Basic.lean
/- Copyright (c) 2021 Julian Kuelshammer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Julian Kuelshammer -/ import Mathlib.Algebra.PEmptyInstances import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.CategoryTheory.Elementwise import Mathlib.CategoryTheory.Functor...
Instances.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique import Mathlib.Analy...
FormalMultilinearSeries.lean
/- Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ import Mathlib.Analysis.NormedSpace.Multilinear.Curry /-! # Formal multilinear series In this file we define `FormalMultilinearSeries π•œ E F` to be a family o...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
Formula.lean
/- Copyright (c) 2025 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.Affine.Basic /-! # Negation and addition formulae for nonsingular points in affine coordinates Le...
DSlope.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.Analysis.Calculus.Deriv.Slope import Mathlib.Analysis.Calculus.Deriv.Comp import Mathlib.Analysis.Calculus.FDeriv.Add import Mathlib.Analysis.Calculu...
Disjoint.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura -/ import Mathlib.Data.Set.Basic /-! # Theorems about the `Disjoint` relation on `Set`. -/ assert_not_exists HeytingAlgebra RelIso /-! ### Set coerci...
Sym.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.Data.Nat.Choose.Basic import Mathlib.Data.Sym.Sym2 /-! # Unordered tuples of elements of a list Defines `List.sym` and the specialized `List.sym2` for comp...
Basic.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.FunLike.Basic import Mathlib.Logic.Embedding.Basic import Mathlib.Order.RelClasses /-! # Relation homomorphisms, embeddings, isomorphisms This f...
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...
Angle.lean
/- Copyright (c) 2024 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic /-! # Angle between complex numbers This file rel...
nilpotent.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 div bigop prime finset fingroup morphism. Fro...
Imo2006Q5.lean
/- Copyright (c) 2022 Violeta HernΓ‘ndez Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta HernΓ‘ndez Palacios -/ import Mathlib.Algebra.Polynomial.Roots import Mathlib.Dynamics.PeriodicPts.Lemmas /-! # IMO 2006 Q5 Let $P(x)$ be a polynomial of degree $n...
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.
SuperFactorial.lean
/- Copyright (c) 2023 Moritz Firsching. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Firsching -/ import Mathlib.Algebra.BigOperators.Intervals import Mathlib.Algebra.Polynomial.Monic import Mathlib.Data.Nat.Factorial.Basic import Mathlib.LinearAlgebra.Vanderm...
Finmap.lean
/- Copyright (c) 2018 Sean Leather. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sean Leather, Mario Carneiro -/ import Mathlib.Data.List.AList import Mathlib.Data.Finset.Sigma import Mathlib.Data.Part /-! # Finite maps over `Multiset` -/ universe u v w open List ...
TransfiniteIteration.lean
/- Copyright (c) 2024 JoΓ«l Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: JoΓ«l Riou -/ import Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty import Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition import Mathlib.CategoryTheory.Limits.Shapes.P...
Absorbs.lean
/- Copyright (c) 2020 Jean Lo, Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Yury Kudryashov -/ import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set import Mathlib.Algebra.Ring.Action.Pointwise.Set import Mathlib.Topology.Bornology.Basic...
abelian.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 choice div fintype finfun bigop finset prime. From ma...
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. (******************************************************...
FinBddDistLat.lean
/- Copyright (c) 2022 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ import Mathlib.Data.Fintype.Order import Mathlib.Order.Category.BddDistLat import Mathlib.Order.Category.FinPartOrd /-! # The category of finite bounded distributive lat...
Filter.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.Filter.Lift import Mathlib.Order.Interval.Set.Monotone import Mathlib.Topology.Separation.Basic /-! # Topology on the set of filters on a type...
Wronskian.lean
/- Copyright (c) 2024 Jineon Baek and Seewoo Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jineon Baek, Seewoo Lee -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative import Mathlib.LinearAlgebra.SesquilinearForm import Ma...
Projection.lean
import Mathlib.Analysis.InnerProductSpace.Projection.Basic import Mathlib.Analysis.InnerProductSpace.Projection.FiniteDimensional import Mathlib.Analysis.InnerProductSpace.Projection.Minimal import Mathlib.Analysis.InnerProductSpace.Projection.Reflection import Mathlib.Analysis.InnerProductSpace.Projection.Submodule d...
orderedzmod.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...