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all_character.v
From mathcomp Require Export character. From mathcomp Require Export classfun. From mathcomp Require Export inertia. From mathcomp Require Export integral_char. From mathcomp Require Export mxabelem. From mathcomp Require Export mxrepresentation. From mathcomp Require Export vcharacter.
HashMap.lean
/- Copyright (c) 2024 Lean FRO. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Std.Data.HashMap.Basic import Mathlib.Init /-! # Convenience functions for hash maps These will be reimplemented in the Lean standard library. -/ namespace Std.Hash...
ImproperIntegrals.lean
/- Copyright (c) 2023 David Loeffler. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.JapaneseBracket import Mathlib.Analysis.SpecialFunctions.Integrals.Basic import Mathlib.MeasureTheory.Group.Integral import M...
AEStabilizer.lean
/- Copyright (c) 2024 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.MeasureTheory.Group.Action import Mathlib.Order.Filter.EventuallyConst /-! # A.e. stabilizer of a set In this file we define the a.e. stabilizer of...
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....
LinearRecurrence.lean
/- Copyright (c) 2020 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ import Mathlib.Algebra.Polynomial.Eval.Defs import Mathlib.LinearAlgebra.Dimension.Constructions /-! # Linear recurrence Informally, a "linear recurrence" is an...
BaseChange.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Algebra.Lie.TensorProduct /-! # Extension and restriction of scalars for Lie algebras and Lie modules Lie al...
ssralg.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 choice fintype finf...
Nat.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson -/ import Mathlib.Algebra.GCDMonoid.Basic import Mathlib.Algebra.Order.Group.Unbundled.Int import Mathlib.Algebra.Ring.Int.Units import M...
Finsupp.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios, Junyan Xu -/ import Mathlib.SetTheory.Cardinal.Arithmetic import Mathlib.Data.Finsupp.Basic import Mathlib.Data.Finsupp.Multiset /-! # Results ...
Basic.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.Algebra.Category.MonCat.Basic import Mathlib.CategoryTheory.Monoidal.CommMon_ import Mathlib.CategoryTheory.Monoidal.Types.Basic /-! # `Mon_ (Type u) ≌ Mo...
Tower.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Yuyang Zhao -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.Algebra.Polynomial.AlgebraMap /-! # Algebra towers for polynomial This file proves some basic results about t...
ColumnRowPartitioned.lean
/- Copyright (c) 2023 Mohanad ahmed. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mohanad Ahmed -/ import Mathlib.Data.Matrix.Block import Mathlib.LinearAlgebra.Matrix.SemiringInverse /-! # Block Matrices from Rows and Columns This file provides the basic definiti...
Verification.lean
/- Copyright (c) 2020 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis -/ import Mathlib.Tactic.Linarith.Parsing import Mathlib.Util.Qq /-! # Deriving a proof of false `linarith` uses an untrusted oracle to produce a certificate of uns...
Filtered.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Justus Springer -/ import Mathlib.CategoryTheory.Limits.Preserves.Basic import Mathlib.CategoryTheory.Filtered.Basic /-! # Preservation of filtered colimits and cofiltered...
HomologicalComplexLimits.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.Single import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits import Mathlib.CategoryTheory.Limits.Preserves.Finite import Mathlib.CategoryThe...
Nakayama.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.RingTheory.Finiteness.Basic import Mathlib.RingTheory.Finiteness.Nakayama import Mathlib.RingTheory.Jacobson.Ideal /-! # Nakayama's lemma This file conta...
UniversallyClosed.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion import Mathlib.AlgebraicGeometry.PullbackCarrier import Mathlib.Topology.LocalAtTarget /-! # Universally closed ...
ssrnat.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From Corelib Require Import PosDef. From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype. #[export] Set Warnings "-ov...
FinitePlaces.lean
/- Copyright (c) 2024 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fabrizio Barroero -/ import Mathlib.Data.Int.WithZero import Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings import Mathlib.RingTheory.DedekindDomain.AdicValuation import ...
Pairing.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Sophie Morel -/ import Mathlib.LinearAlgebra.ExteriorPower.Basic import Mathlib.LinearAlgebra.TensorPower.Pairing /-! # The pairing between the exterior power of the dual and t...
Estimator.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.Data.Set.Operations import Mathlib.Order.Heyting.Basic import Mathlib.Order.RelClasses import Mathlib.Order.Hom.Basic import Mathlib.Lean.Thunk /-! # Impr...
ContinuantsRecurrence.lean
/- Copyright (c) 2019 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Algebra.ContinuedFractions.Translations /-! # Recurrence Lemmas for the Continuants (`conts`) Function of Continued Fractions ## Summary Given a...
Encoding.lean
/- Copyright (c) 2022 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson -/ import Mathlib.Computability.Encoding import Mathlib.Logic.Small.List import Mathlib.ModelTheory.Syntax import Mathlib.SetTheory.Cardinal.Arithmetic /-! # Encodings ...
NNReal.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Sébastien Gouëzel, Rémy Degenne, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Power function...
LocallyClosed.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.Constructions import Mathlib.Tactic.TFAE /-! # Locally closed sets ## Main definitions * `IsLocallyClosed`: Predicate saying that a set is locall...
casesm.lean
import Mathlib.Tactic.CasesM set_option autoImplicit true set_option linter.unusedVariables false set_option linter.unusedTactic false in example (h : a ∧ b ∨ c ∧ d) (h2 : e ∧ f) : True := by casesm* _∨_, _∧_ · clear ‹a› ‹b› ‹e› ‹f›; (fail_if_success clear ‹c›); trivial · clear ‹c› ‹d› ‹e› ‹f›; trivial example...
Ordinal.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.Cardinal.Arithmetic import Mathlib.SetTheory.Ordinal.Principal /-! # Ordinal arithmetic with cardinals This file co...
Defs.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Yuyang Zhao -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Basic /-! # Ordered monoids This file provides the defin...
tuple.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. From mathcomp Require Import seq choice fintype path. S...
Hamming.lean
/- Copyright (c) 2022 Wrenna Robson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Wrenna Robson -/ import Mathlib.Analysis.Normed.Group.Basic /-! # Hamming spaces The Hamming metric counts the number of places two members of a (finite) Pi type differ. The Hamming n...
Inner.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.Analysis.InnerProductSpace.Continuous import Mathlib.MeasureTheory.Constructions.BorelSpace.Complex /-! # Measurability of scalar products -/ vari...
EndoFunctor.lean
/- Copyright (c) 2022 Julian Kuelshammer. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Julian Kuelshammer -/ import Mathlib.CategoryTheory.Preadditive.Basic import Mathlib.CategoryTheory.Endofunctor.Algebra import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor /...
Pointwise.lean
/- Copyright (c) 2021 Eric Weiser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.Ring.Subring.Pointwise /-! # Pointwise actions on subalgebras. If `R'` acts on an `R`-algebra `A`...
Deriv.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.Deriv.ZPow import Mathlib.Analysis.SpecialFunctions.Sqrt import Mathlib.Analysis.SpecialFunctions.Log.Deriv impo...
Prod.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Order.UpperLower.Closure /-! # Upper and lower set product The Cartesian product of sets carries over to upper and lower sets i...
Left.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.Monad.Adjunction import Mathlib.CategoryTheory.Monad.Coequalizer /-! # Adjoint lifting This file gives two constructions for building left...
Divisors.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.IsPrimePow import Mathlib.Algebra.Order.BigOperators.Group.Finset import Mathlib.Algebra.Order.Interval.Finset.SuccPred import Mathlib.Algebra....
Cofix.lean
/- Copyright (c) 2018 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Simon Hudon -/ import Mathlib.Control.Functor.Multivariate import Mathlib.Data.PFunctor.Multivariate.Basic import Mathlib.Data.PFunctor.Multivariate.M import Mathlib.Data...
MinImports.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 ImportGraph.Imports import Mathlib.Tactic.MinImports /-! # The `minImports` linter The `minImports` linter incrementally computes the minimal imports needed fo...
WellFoundedSet.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.Prod.Lex import Mathlib.Data.Sigma.Lex import Mathlib.Order.RelIso.Set import Mathlib.Order.WellQuasiOrder import Mathlib.Tactic.TFAE /-! # Well-...
WSeq.lean
/- Copyright (c) 2017 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.WSeq.Basic import Mathlib.Data.WSeq.Defs import Mathlib.Data.WSeq.Productive import Mathlib.Data.WSeq.Relation deprecated_module (since :=...
Replicate.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.AddSub /-! # Repeating elements in multisets ## Main definitions * `replicate n a` is the multiset containing only `a` with mul...
quotient.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype prim...
Affine.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.QuasiSeparated import Mathlib.AlgebraicGeometry.Morphisms.IsIso /-! # Affine morphisms of schemes A morphism of schemes `f : X...
Sieves.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.CategoryTheory.Subpresheaf.Basic import Mathlib.CategoryTheory.Sites.IsSheafFor /-! # Sieves attached to subpresheaves Given a subpresheaf `G` of a preshea...
ColimitTypeFiltered.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.Filtered.Basic import Mathlib.CategoryTheory.Limits.Types.ColimitType /-! # Filtered colimits of types In this file, given a functor `F : J ⥤ Ty...
Algebraize.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Nick Kuhn, Arend Mellendijk, Christian Merten, Calle Sönne, Adam Topaz -/ import Mathlib.Algebra.Algebra.Tower /-! ## Algebraize tactic This file defines the `algebrai...
Defs.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, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis, Heather Macbeth -/ import Mathlib.Algebra.Module.Submodule.Lattice import Mathlib.Algebra.Group.Point...
pairwise_disjoint.lean
import Mathlib abbrev S1 : Fin 3 → Finset (Fin 4) | 0 => {0} | 1 => {1} | 2 => {2, 3} attribute [grind _=_] LawfulSingleton.insert_emptyc_eq attribute [grind =] Finset.mem_singleton attribute [grind =] Finset.disjoint_insert_left attribute [grind =] Finset.disjoint_insert_right attribute [grind] Finset.disjoi...
Defs.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Filter import Mathlib.Data.Finite.Defs /-! # Finite types This file defines a typeclass to state that a type is finite. ## Main declarat...
all_field.v
From mathcomp Require Export algC. From mathcomp Require Export algebraics_fundamentals. From mathcomp Require Export algnum. From mathcomp Require Export closed_field. From mathcomp Require Export cyclotomic. From mathcomp Require Export falgebra. From mathcomp Require Export fieldext. From mathcomp Require Export fin...
Centroid.lean
/- Copyright (c) 2020 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic import Mathlib.LinearAlgebra.AffineSpace.Centroid /-! # Centroid of a simplex in affine space This file proves so...
Arithmetic.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.MeasureTheory.Measure.AEMeasurable /-! # Typeclasses for measurability of operations In this file we define classes `MeasurableMul` etc and prove d...
Pullback.lean
/- Copyright (c) 2023 Floris van Doorn, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn, Heather Macbeth -/ import Mathlib.Geometry.Manifold.ContMDiffMap import Mathlib.Geometry.Manifold.VectorBundle.Basic /-! # Pullbacks of `C^n` vect...
Basic.lean
/- Copyright (c) 2020 Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning, Patrick Lutz -/ import Mathlib.Algebra.Algebra.Subalgebra.Directed import Mathlib.Algebra.Algebra.Subalgebra.IsSimpleOrder import Mathlib.FieldTheory.Se...
EqHaar.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, Sébastien Gouëzel -/ import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas import Mathlib.MeasureTheory.Constructions.BorelSpace.Metric import Mathlib.MeasureTheory...
Decl.lean
/- Copyright (c) 2024 Tomáš Skřivan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Tomáš Skřivan -/ import Mathlib.Init /-! ## `funProp` environment extension that stores all registered function properties -/ namespace Mathlib open Lean Meta namespace Meta.FunProp...
Opposite.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Adam Topaz, Johan Commelin, Joël Riou -/ import Mathlib.Algebra.Group.TransferInstance import Mathlib.Algebra.Module.Equiv.Defs import Mathlib.Algebra.Module.Opposite impor...
output.v
From mathcomp Require Import all_boot all_order all_algebra all_field all_character all_fingroup all_solvable. Open Scope group_scope. Check @cyclic_pgroup_Aut_structure.
List.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Floris van Doorn, Sébastien Gouëzel, Alex J. Best -/ import Mathlib.Algebra.GroupWithZero.Commute import Mathlib.Algebra.GroupWithZero.Divisibility import Mathlib.Algeb...
Subscheme.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.AlgebraicGeometry.Morphisms.Preimmersion import Mathlib.AlgebraicGeometry.IdealSheaf.Basic import Mathlib.CategoryTheory.Adjunction.Opposites /-! # Subschem...
Defs.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.TwoSidedIdeal.Lattice import Mathlib.Order.Atoms /-! # Simple rings A ring `R` is **simple** if it has only two two-sided ideals, namely `⊥` ...
Rat.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.Field.Opposite import Mathlib.Algebra.Star.Basic import Mathlib.Data.NNRat.Defs import Mathlib.Data.Rat.Cast.Defs /-! # *-ring structure on ℚ and ...
Quotient.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.Localization.LocalizerMorphism import Mathlib.CategoryTheory.Quotient /-! # Localization of quotient categories Given a relation `homRel : HomRe...
DependsOn.lean
/- Copyright (c) 2024 Etienne Marion. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Etienne Marion -/ import Mathlib.Data.Set.Restrict /-! # Functions depending only on some variables When dealing with a function `f : Π i, α i` depending on many variables, some oper...
ssrint.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import fintype finfun b...
MvPolynomial.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.LinearAlgebra.Dimension.Finite import Mathlib.LinearAlgebra.Dimension.StrongRankCondition import Mathlib.L...
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...
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....
Reflection.lean
/- Copyright (c) 2023 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash, Deepro Choudhury, Mitchell Lee, Johan Commelin -/ import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Algebra.Module.Linear...
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. ...
Fin2.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Data.Finset.Image import Mathlib.Data.Fintype.Defs import Mathlib.Data.Nat.Notation import Mathlib.Logic.Function.Basic /-! # Inductive type variant o...
Curry.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Brendan Murphy -/ import Mathlib.Data.Fin.Tuple.Basic import Mathlib.Logic.Equiv.Fin.Basic import Mathlib.Logic.Function.OfArity /-! # Currying and uncurrying of n-ary funct...
Field.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.Polynomial.Splits import Mathlib.RingTheory.Adjoin.Basic import Mathlib.RingTheory.AdjoinRoot /-! # Adjoining elements to a field Some lemmas on ...
all_field.v
From mathcomp Require Export algC. From mathcomp Require Export algebraics_fundamentals. From mathcomp Require Export algnum. From mathcomp Require Export closed_field. From mathcomp Require Export cyclotomic. From mathcomp Require Export falgebra. From mathcomp Require Export fieldext. From mathcomp Require Export fin...
CartesianClosed.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.Closed.Types import Mathlib.CategoryTheory.Sites.CartesianClosed import Mathlib.CategoryTheory.Sites.Equivalence import Mathlib.Cond...
ssrnotations.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) (******************************************************************************) (* - Reserved notation for various arithmetic and algebraic operations: ...
GaussNorm.lean
/- Copyright (c) 2025 Fabrizio Barroero. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Fabrizio Barroero -/ import Mathlib.RingTheory.PowerSeries.GaussNorm /-! # Gauss norm for polynomials This file defines the Gauss norm for polynomials. Given a polynomial `p` in `...
Colim.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.Filtered.Final import Mathlib.CategoryTheory.Limits.Connected import Mathlib.CategoryTheory.MorphismProperty.Limits import Mathlib.CategoryTheory....
Circulant.lean
/- Copyright (c) 2024 Iván Renison, Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Iván Renison, Bhavik Mehta -/ import Mathlib.Algebra.Group.Fin.Basic import Mathlib.Combinatorics.SimpleGraph.Hasse import Mathlib.Algebra.Group.Pointwise.Set.Basic /-! # ...
Denumerable.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.Algebra.Ring.Rat import Mathlib.Data.Rat.Encodable import Mathlib.Algebra.CharZero.Infinite import Mathlib.Logic.Denumerable /-! # Denumerability of ℚ Th...
AbsolutelyContinuous.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.Measure.Map /-! # Absolute Continuity of Measures We say that `μ` is absolutely continuous with respect to `ν`, or that...
SmoothingSeminorm.lean
/- Copyright (c) 2024 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.Algebra.Order.GroupWithZero.Bounds import Mathlib.Analysis.Normed.Unbundled.RingSeminorm import Mathlib.Analysis.Specia...
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, Johan Commelin, Mario Carneiro -/ import Mathlib.Algebra.Algebra.Subalgebra.Lattice import Mathlib.Algebra.Algebra.Tower import Mathlib.Algebra.GroupWithZero.Divisibili...
Pi.lean
/- Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel -/ import Mathlib.Data.ENNReal.Lemmas import Mathlib.Topology.Bornology.Constructions import Math...
DirectLimitFG.lean
/- Copyright (c) 2025 Antoine Chambert-Loir and María-Inés de Frutos Fernández. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir, María-Inés de Frutos Fernández -/ import Mathlib.LinearAlgebra.TensorProduct.DirectLimit import Mathlib.LinearAlgebra....
Real.lean
/- Copyright (c) 2024 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto, Oliver Butterley -/ import Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic import Mathlib.MeasureTheory.Integral.Bochner.Set import Mathlib.Order.Interval.Set.Unio...
interval.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 div fintype bigo...
ViaEmbedding.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, Mario Carneiro -/ import Mathlib.Algebra.Group.End import Mathlib.Logic.Embedding.Basic import Mathlib.Logic.Equiv.Set /-! # `Equiv.Perm.viaEmbedding`, a non...
Notations.lean
/- Copyright (c) 2022 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.AlternatingFaceMapComplex /-! # Notations for the Dold-Kan equivalence This file defines the notation `K[X] : ChainComplex C ℕ` for the alte...
Compacts.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, Yaël Dillies -/ import Mathlib.Topology.Sets.Closeds import Mathlib.Topology.QuasiSeparated /-! # Compact sets We define a few types of compact sets in a topologi...
Algebra.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Order.Module.Defs import Mathlib.Tactic.Positivity.Core /-! # Ordered algebras This file proves properties of...
RelSeries.lean
/- Copyright (c) 2023 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Fangming Li -/ import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Data.Fin.VecNotation import Mathlib.Data.Fintype.Pi import Mathlib.Data.Fintype.Pigeonhole import Mathli...
interval.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 div fintype bigo...
aesop_cat.lean
import Mathlib.CategoryTheory.Category.Basic structure Foo where x : Nat w : x = 37 := by cat_disch /-- warning: declaration uses 'sorry' -/ #guard_msgs in example : Foo where x := sorry /-- error: could not synthesize default value for field 'w' of 'Foo' using tactics --- error: tactic 'aesop' failed, failed ...
RightDerived.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Kim Morrison, Joël Riou -/ import Mathlib.Algebra.Homology.Additive import Mathlib.CategoryTheory.Abelian.Injective.Resolution /-! # Right-derived functors We define the ...
AbsConvexOpen.lean
/- Copyright (c) 2022 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ import Mathlib.Analysis.LocallyConvex.AbsConvex import Mathlib.Analysis.LocallyConvex.WithSeminorms import Mathlib.Analysis.Convex.Gauge /-! # Absolutely convex open sets ...
IsFinite.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.Algebra.Category.Grp.Abelian import Mathlib.Algebra.Category.Grp.EpiMono import Mathlib.Algebra.Category.Grp.Zero import Mathlib.Algebra.Homology.ShortComplex.Ab...
Braiding.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.GradedObject.Monoidal import Mathlib.CategoryTheory.Monoidal.Braided.Basic /-! # The braided and symmetric category structures on graded objects ...