filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
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
... |
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