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Unitary.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.Tactic.Peel import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital import Mathlib.Analysis.Complex.Basic /-! # Conditions on unitary e...
Dual.lean
/- Copyright (c) 2025 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Module.Submodule.Pointwise import Mathlib.Geometry.Convex.Cone.Pointed /-! # The algebraic dual of a cone Given a bilinear pairing `p` between tw...
Ray.lean
/- Copyright (c) 2021 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Order.Module.Algebra import Mathlib.Algebra.Ring.Subring.Units import Mathlib.LinearAlgebra.LinearIndepende...
List.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Topology.Constructions import Mathlib.Order.Filter.ListTraverse import Mathlib.Tactic.AdaptationNote import Mathlib.Topology.Algebra.Monoid.Defs /-! # To...
End.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Yury Kudryashov -/ import Mathlib.Algebra.Group.Action.Basic import Mathlib.Algebra.Group.Action.Hom import Mathlib.Algebra.Group.End /-! # Interaction between actions and...
Shapes.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.Limits.Shapes.Multiequalizer import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Shapes.Pullback...
MinimalAxioms.lean
/- Copyright (c) 2015 Nathaniel Thomas. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nathaniel Thomas, Jeremy Avigad, Johannes Hölzl, Mario Carneiro, Martin C. Martin -/ import Mathlib.Algebra.Module.Defs /-! # Minimal Axioms for a Module This file defines a constr...
Quasicoherent.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.Sheaf.Generators /-! # Quasicoherent sheaves A sheaf of modules is quasi-coherent if it admits locally a presentation as the cokerne...
polyXY.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype tuple fi...
Basic.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kyle Miller -/ import Lean import Mathlib.Tactic.PPWithUniv import Mathlib.Tactic.ExtendDoc import Mathlib.Tactic.Lemma import Mathlib.Tactic.TypeStar import Mathlib.Ta...
Homology.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.Algebra.Homology.ShortComplex.RightHomology /-! # Homology of short complexes In this file, we shall define the homology of short complexes `S`, i.e. diagrams...
Nilpotent.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.RingTheory.Finiteness.Basic import Mathlib.RingTheory.Nilpotent.Lemmas /-! # Nilpotent maps on finite modules -/ variable {R M : Type*} [CommSemirin...
Basic.lean
/- Copyright (c) 2025 Nailin Guan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Nailin Guan -/ import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.Order.Ring.Int import Mathlib.Algebra.GradedMonoid import Mathlib.Algebra.Group.Submonoid.Defs import Mathlib.Alge...
ShiftedLegendre.lean
/- Copyright (c) 2025 Junqi Liu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junqi Liu, Jinzhao Pan -/ import Mathlib.Algebra.Polynomial.AlgebraMap import Mathlib.Algebra.Polynomial.Derivative /-! # shifted Legendre Polynomials In this file, we define the shifted ...
NormedSpace.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.ContMDiff.Constructions import Mathlib.Analysis.NormedSpace.OperatorNorm.Prod /-! ## Equivalence of smoothne...
Extend.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.Embedding.IsSupported import Mathlib.Algebra.Homology.Additive import Mathlib.Algebra.Homology.Opposite /-! # The extension of a homological co...
extremal.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div. From mathcomp Require Import choice fintype bigo...
HasLimits.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Mario Carneiro, Kim Morrison, Floris van Doorn -/ import Mathlib.CategoryTheory.Limits.IsLimit import Mathlib.CategoryTheory.Category.ULift import Mathlib.CategoryTheory.Ess...
Counterexamples.lean
import Counterexamples.AharoniKorman import Counterexamples.CanonicallyOrderedCommSemiringTwoMul import Counterexamples.CharPZeroNeCharZero import Counterexamples.CliffordAlgebraNotInjective import Counterexamples.Cyclotomic105 import Counterexamples.DirectSumIsInternal import Counterexamples.DiscreteTopologyNonDiscret...
Basic.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Kevin Buzzard -/ import Mathlib.CategoryTheory.Preadditive.Projective.Basic /-! # Injective objects and categories with enough injectives An object `J` is injective iff e...
CompleteSublattice.lean
/- Copyright (c) 2024 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Data.Set.Functor import Mathlib.Order.Sublattice import Mathlib.Order.Hom.CompleteLattice /-! # Complete Sublattices This file defines complete sublattices...
MeanErgodic.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.Analysis.InnerProductSpace.Projection.Submodule import Mathlib.Dynamics.BirkhoffSum.NormedSpace /-! # Von Neumann Mean Ergodic Theorem in a Hilbert ...
pgroup.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 bigop finset prime fingroup morphism. From mat...
ContextInfo.lean
/- Copyright (c) 2025 Lean FRO, LLC. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstring. import Mathlib.Tactic.Linter.Header /-! # Executing acti...
PNatPowAssoc.lean
/- Copyright (c) 2023 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Data.PNat.Basic import Mathlib.Algebra.Notation.Prod /-! # Typeclasses for power-associative structures In this file we define power-associativity f...
ErwQuestion.lean
import Mathlib.Tactic.ErwQuestion section Single def f (x : Nat) := x + 1 def a := 37 theorem f_a : f a = 38 := rfl def b := a -- make sure that `erw'` is noisy, so that it gets picked up by CI /-- info: Debugging `erw?` -/ #guard_msgs in example : f 37 = 38 := by erw? [f] /-- error: Tactic `rewrite` failed: Did ...
PathELength.lean
/- Copyright (c) 2025 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.AddTorsor.AffineMap import Mathlib.Analysis.SpecialFunctions.SmoothTransition import Mathlib.Geometry.Manifold.ContMDiff.Normed...
Basic.lean
/- Copyright (c) 2025 Richard Hill. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Richard Hill, Andrew Yang -/ import Mathlib.Algebra.Category.ModuleCat.Topology.Homology import Mathlib.Algebra.Homology.Embedding.Restriction import Mathlib.Algebra.Homology.Functor imp...
Algebra.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.Algebra.Defs import Mathlib.Algebra.DirectSum.Module import Mathlib.Algebra.DirectSum.Ring /-! # Additively-graded algebra structures on `⨁ i, A i` ...
Caratheodory.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 -/ import Mathlib.MeasureTheory.OuterMeasure.OfFunction import Mathlib.MeasureTheory.PiSystem /-! # The Caratheodory σ-algebra of an outer measure Give...
Relative.lean
/- Copyright (c) 2025 Jeremy Tan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Tan -/ import Mathlib.Data.Set.Image import Mathlib.Data.SetLike.Basic import Mathlib.Order.Interval.Set.Defs import Mathlib.Order.SetNotation /-! # Properties of relative upper/lo...
Basic.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn, Heather Macbeth -/ import Mathlib.Topology.FiberBundle.Trivialization import Mathlib.Topology.Order.LeftRightNhds /-! # Fiber bundles Mathemat...
JacobsonSpace.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.Topology.LocalAtTarget import Mathlib.Topology.Separation.Regular import Mathlib.Tactic.StacksAttribute /-! # Jacobson spaces ## Main results - `JacobsonS...
Zify.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll, Robert Y. Lewis -/ import Mathlib.Tactic.Zify import Mathlib.Algebra.Ring.Int.Parity import Mathlib.Algebra.Ring.Int.Units set_option linter.unusedVariables false private ...
Horn.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kim Morrison, Adam Topaz, Joël Riou -/ import Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex import Mathlib.CategoryTheory.Subpresheaf.Equalizer /-! # Horns This fi...
ArzelaAscoli.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth -/ import Mathlib.Topology.ContinuousMap.Bounded.Basic import Mathlib.Topology.MetricSpace.Equicontinuity /-! # ...
Atlas.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Floris van Doorn -/ import Mathlib.Geometry.Manifold.ContMDiff.Basic /-! ## Smoothness of charts and local structomorphisms We show that the model with corners,...
NonZeroDivisors.lean
/- Copyright (c) 2022 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Algebra.GroupWithZero.NonZeroDivisors import Mathlib.Algebra.Regular.Basic import Mathlib.Algebra.Ring.Basic /-! # Non-zero divisors in a ring -/ a...
test_regular_conv.v
From mathcomp Require Import all_boot all_order all_algebra all_field. Section regular. Import GRing. Goal forall R : ringType, [the lalgType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : comRingType, [the algType R of R^o] = R :> ringType. Proof. by move=> [? []]. Qed. Goal forall R : c...
PadicNorm.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 -/ import Mathlib.Algebra.Order.AbsoluteValue.Basic import Mathlib.NumberTheory.Padics.PadicVal.Basic /-! # p-adic norm This file defines the `p`-adic norm on `ℚ`. ...
Different.lean
/- Copyright (c) 2025 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.NumberTheory.NumberField.Discriminant.Defs import Mathlib.RingTheory.DedekindDomain.Factorization import Mathlib.RingTheory.DedekindDomain.Different import M...
qpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple bigop binomial finset finfun ssralg. From mathcomp Require Import countalg finalg poly polydiv perm fingroup matrix. From mathcomp Require Import mxalgebra mxpoly...
TotallyBounded.lean
/- Copyright (c) 2024 Christopher Hoskin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christopher Hoskin -/ import Mathlib.Topology.UniformSpace.Cauchy import Mathlib.Analysis.Convex.Hull import Mathlib.Topology.Algebra.IsUniformGroup.Basic import Mathlib.Topology....
OfAdjunction.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Adjunction.Opposites import Mathlib.CategoryTheory.Adjunction.FullyFaithful import Mathlib.CategoryTheory.Localization.CalculusOfFractions /-! # ...
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.
Images.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Markus Himmel -/ import Mathlib.CategoryTheory.Limits.Shapes.Equalizers import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono import Mathlib.CategoryTheory.Limits.Shape...
DynamicalEntourage.lean
/- Copyright (c) 2024 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine, Pietro Monticone -/ import Mathlib.Order.Interval.Finset.Nat import Mathlib.Topology.Constructions.SumProd import Mathlib.Topology.UniformSpace.Basic /-! # Dynamical e...
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 ...
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, Johan Commelin, Kim Morrison -/ import Mathlib.CategoryTheory.Limits.Constructions.Pullbacks import Mathlib.CategoryTheory.Preadditive.Biproducts import Mathlib.CategoryT...
Generators.lean
import Mathlib.RingTheory.Extension.Generators deprecated_module (since := "2025-05-11")
Class.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.SetTheory.ZFC.Ordinal /-! # ZFC classes Classes in set theory are usually defined as collections of elements satisfying some property. Here, however,...
WellKnown.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Algebra.Algebra.Rat import Mathlib.Data.Nat.Cast.Field import Mathlib.RingTheory.PowerSeries.Basic /-! # Definition of well-known power series In t...
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...
Prod.lean
/- Copyright (c) 2023 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Divisibility.Basic import Mathlib.Algebra.Group.Pi.Basic import Mathlib.Algebra.Group.Prod import Mathlib.Tactic.Common /-! # Lemmas about the...
QuotientRing.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.RingTheory.Ideal.Quotient.Operations import Mathlib.RingTheory.Int.Basic import Mathlib.RingTheory.ZMod /-! # `ZMod n` and quotient groups / rings This fil...
Algebra.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Nicolò Cavalleri -/ import Mathlib.Algebra.Algebra.Pi import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Tactic.FieldSimp import Mathlib.Topology.Algebra.Infini...
Basic.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Data.Int.Init import Mathlib.Data.Nat.Basic import Mathlib.Logic.Nontrivial.Defs import Mathlib.Tactic.Convert import Mathlib.Tactic.Lift import Mathlib....
Destutter.lean
/- Copyright (c) 2022 Eric Rodriguez. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Rodriguez, Eric Wieser -/ import Mathlib.Data.List.Chain /-! # Destuttering of Lists This file proves theorems about `List.destutter` (in `Data.List.Defs`), which greedily remov...
VonNeumann.lean
/- Copyright (c) 2024 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.SetTheory.ZFC.Class import Mathlib.SetTheory.ZFC.Ordinal import Mathlib.SetTheory.ZFC.Rank /-! # Von Neumann hierarchy This f...
Variable.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.Init import Lean.Meta.Tactic.TryThis /-! # The `variable?` command This defines a command like `variable` that automatically adds all missing typeclass arg...
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) 2022 Jesse Reimann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jesse Reimann, Kalle Kytölä -/ import Mathlib.MeasureTheory.Measure.Content import Mathlib.Topology.ContinuousMap.CompactlySupported import Mathlib.Topology.PartitionOfUnity /-! # Rie...
Imo1998Q2.lean
/- Copyright (c) 2020 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Field.Basic import Mathlib.Algebra.Order.Field.Rat import Mathlib.Data.Finite.Prod impor...
ITauto.lean
/- Copyright (c) 2021 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Batteries.Tactic.Exact import Batteries.Tactic.Init import Mathlib.Logic.Basic import Mathlib.Util.AtomM import Qq /-! # Intuitionistic tautology (`itauto`) ...
LocallyFinite.lean
/- Copyright (c) 2024 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.BigOperators.Group.Finset.Sigma import Mathlib.Algebra.Order.Interval.Finset.SuccPred import Mathlib.Data.Nat.SuccPred import Mathlib.Order.Interva...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
FirstMainTheorem.lean
/- Copyright (c) 2025 Stefan Kebekus. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Stefan Kebekus -/ import Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction /-! # The First Main Theorem of Value Distribution Theory The First Main Theorem of Value D...
Limits.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.Condensed.Module /-! # Limits in categories of condensed objects This file adds some instances for limits in condensed sets and condensed module...
ssrAC.v
From HB Require Import structures. From Corelib Require Import PosDef. (* use #[warning="-hiding-delimiting-key"] attribute once we require Coq 8.18 *) (* (the warning was completely removed in 9.0) *) Set Warnings "-hiding-delimiting-key". From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq bigop. ...
CommDiag.lean
import Mathlib.Tactic.Widget.CommDiag import ProofWidgets.Component.Panel.SelectionPanel import ProofWidgets.Component.Panel.GoalTypePanel /-! ## Example use of commutative diagram widgets -/ universe u namespace CategoryTheory open ProofWidgets /-- Local instance to make examples work. -/ local instance : Category ...
all_ssreflect.v
Attributes deprecated(since="mathcomp 2.5.0", note="Use 'all_boot' and/or 'all_order' instead."). From mathcomp Require Export all_boot. From mathcomp Require Export preorder. From mathcomp Require Export order.
TransImports.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Mathlib.Init /-! # The `#trans_imports` command `#trans_imports` reports how many transitive imports the current module has. The command takes an optional str...
Topology.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.Analysis.Filter import Mathlib.Topology.Bases import Mathlib.Topology.LocallyFinite /-! # Computational realization of topological spaces (experi...
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 ...
SpinGroup.lean
/- Copyright (c) 2022 Jiale Miao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiale Miao, Utensil Song, Eric Wieser -/ import Mathlib.Algebra.Ring.Action.ConjAct import Mathlib.GroupTheory.GroupAction.ConjAct import Mathlib.Algebra.Star.Unitary import Mathlib.Linear...
IsIntegral.lean
/- Copyright (c) 2022 Yuyang Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuyang Zhao -/ import Mathlib.Analysis.Complex.Basic import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic /-! # Integral elements of ℂ This file proves that `Complex.I` is integr...
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. (************************************************...
Preadditive.lean
/- Copyright (c) 2022 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Generator.Basic import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic /-! # Separators in preadditive categories This file contains cha...
Internal.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang, Fangming Li -/ import Mathlib.Algebra.Algebra.Operations import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.DirectSum.Algebra...
morphism.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 choice. From mathcomp Require Import fintype finfun bigop finset fingroup. (***********...
zmodp.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 choice eqtype ssrnat seq. From mathcomp Require Import div fintype bigo...
Defs.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Algebra.Hom import Mathlib.Data.Set.Finite.Lemmas import Mathlib.Data.Finsupp.Defs import Mathlib.GroupTheory.Finiteness import Mathlib.RingThe...
CompMap.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Composition.Comp import Mathlib.Probability.Kernel.Composition.MapComap /-! # Lemmas about compositions and maps of kernels This file ...
Finite.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Data.ULift import Mathlib.Data.ZMod.Defs import Mathlib.SetTheory.Cardinal.ToNat import Mathlib.SetTheory.Cardinal.ENat /-! # Finite Cardinality Funct...
Opposite.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Group.Action.Defs import Mathlib.Algebra.Group.Opposite /-! # Scalar actions on and by `Mᵐᵒᵖ` This file defines the actions on the opposite type `S...
AssertExistsExt.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Lean.Environment import Mathlib.Init /-! # Environment extension for tracking existence of declarations and imports This is used by the `assert_not_exists` an...
IntegralDomain.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Chris Hughes -/ import Mathlib.Algebra.Polynomial.Roots import Mathlib.Data.Fintype.Inv import Mathlib.GroupTheory.SpecificGroups.Cyclic import Mathlib.Tactic.FieldSimp...
OrderedCancelAddCommMonoidWithBounds.lean
/- Copyright (c) 2023 Martin Dvorak. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Dvorak -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.Order.BoundedOrder.Lattice /-! # Do not combine OrderedCancelAddCommMonoid with BoundedOrder This file shows t...
archimedean.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop or...
extraspecial.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 choice fintype bigop finset prime binomial. From mathc...
Quotient.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yuyang Zhao -/ import Mathlib.Data.List.Pi import Mathlib.Data.Fintype.Defs /-! # Quotients of families indexed by a finite type This file proves some basic facts and...
Immersion.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.Preimmersion import Mathlib.AlgebraicGeometry.Morphisms.Separated /-! # Immersions of schemes A morphism of schemes `f : X ⟶ Y...
mxabelem.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...
Translations.lean
/- Copyright (c) 2020 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Computation.Basic import Mathlib.Algebra.ContinuedFractions.Translations import Mathlib.Algebra.Order.Floor.Ring /-! # ...
L2Space.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Analysis.InnerProductSpace.LinearMap import Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions import Mathlib.MeasureTheory.Function.StronglyMeasur...
Basic.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.TensorProduct.RightExactness import Mathlib.RingTheory.Ideal.Cotangent import Mathlib.RingTheory.Localization.Defs /-! # Extension of algebra...
Adjunctions.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.Category.MonCat.Basic import Mathlib.Algebra.Category.Semigrp.Basic import Mathlib.Algebra.FreeMonoid.Basic import Mathlib.Algebra.Grou...
AffineMap.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.Analysis.Calculus.Deriv.Add import Mathlib.Analysis.Calculus.Deriv.Linear import Mathlib.LinearAlgebra.AffineSpace.AffineMap /-! # Derivatives of aff...
Defs.lean
/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon, Keeley Hoek, Floris van Doorn, Chris Bailey -/ import Mathlib.Init /-! # Definitions for `String` This file defines a bunch of functions for the `String` datatype. -/ name...
TransfiniteCompositionOfShape.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.ComposableArrows import Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous import Mathlib.CategoryTheory.Limits.Shapes.Preorder.Fin...