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Ultra.lean
/- Copyright (c) 2024 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Analysis.Normed.Order.Hom.Basic import Mathlib.Topology.MetricSpace.Ultra.Basic /-! # Constructing nonarchimedean (ultrametric) normed groups from n...
prime.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype div bigop. (*************************...
Irreducible.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, Yury Kudryashov -/ import Mathlib.Order.Minimal import Mathlib.Order.Zorn import Mathlib.Topology.ContinuousOn import Mathlib.Tactic.StacksAttribute /-...
Semigrp.lean
import Mathlib.Algebra.Category.Semigrp.Basic universe v u open CategoryTheory Semigrp set_option maxHeartbeats 10000 set_option synthInstance.maxHeartbeats 2000 /- We test if all the coercions and `map_mul` lemmas trigger correctly. -/ example (X : Type u) [Semigroup X] : ⇑(𝟙 (of X)) = id := by simp example {X ...
Selmer.lean
/- Copyright (c) 2022 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.Analysis.Complex.Polynomial.UnitTrinomial import Mathlib.RingTheory.Polynomial.GaussLemma import Mathlib.Tactic.LinearCombination /-! # Irreducibili...
numfield.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import ssrAC div fintyp...
Preimage.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Data.Finset.Preimage import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # Sums and products over preimages of finite sets. -/ assert_not_exis...
Basic.lean
/- Copyright (c) 2019 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Mario Carneiro, Isabel Longbottom, Kim Morrison, Apurva Nakade, Yuyang Zhao -/ import Mathlib.Algebra.Order.Monoid.Defs import Mathlib.SetTheory.PGame.Algebra import Mathl...
AbsMax.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Complex.CauchyIntegral import Mathlib.Analysis.InnerProductSpace.Convex import Mathlib.Analysis.NormedSpace.Extr import Mathlib.Data.Complex...
abelian.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import choice div fintype finfun bigop finset prime. From ma...
InferParam.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Mario Carneiro -/ import Mathlib.Init import Lean.Elab.Tactic.Basic import Lean.Meta.Tactic.Replace /-! # Infer an optional parameter In this file we define a tacti...
seq.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat. (******************************************************...
Catalan.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.Algebra.BigOperators.Fin import Mathlib.Algebra.BigOperators.NatAntidiagonal import Mathlib.Data.Nat.Choose.Central import Mathlib.Tactic.Field...
Basic.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Kim Morrison, Jakob von Raumer -/ import Mathlib.Algebra.Category.ModuleCat.Basic import Mathlib.LinearAlgebra.TensorProduct.Associator import Mathlib.CategoryTheory.Monoi...
Quotient.lean
/- Copyright (c) 2018 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes, Thomas Browning -/ import Mathlib.Algebra.Group.Subgroup.Actions import Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas import Mathlib.Data.Fintype.BigOperators import Mathli...
Formula.lean
/- Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula import Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic /-! # Negation and ...
ToApp.lean
import Mathlib.Tactic.CategoryTheory.ToApp import Mathlib.CategoryTheory.Bicategory.Functor.Prelax universe w v u namespace CategoryTheory.ToAppTest open Bicategory Category variable {B : Type u} [Bicategory.{w, v} B] {a b c d e : B} @[to_app] theorem whiskerLeft_hom_inv (f : a ⟶ b) {g h : b ⟶ c} (η : g ≅ h) : ...
spectral.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat. From mathcomp Require Import seq div fintype bigop ssralg finset fingroup zmodp. From mathcomp Require Import poly polydiv order ssrnum matrix mxalgebra vector. From mathcomp Require Import mxpoly mxred sesqui...
imset2_gproduct.v
From mathcomp Require Import all_boot all_fingroup. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Import GroupScope. Open Scope group_scope. Check @ker_sdprodm.
Lattice.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.Data.Multiset.FinsetOps import Mathlib.Data.Multiset.Fold /-! # Lattice operations on multisets -/ namespace Multiset variable {α : Type*} /-! ###...
Sym.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Data.Finset.Lattice.Fold import Mathlib.Data.Fintype.Vector import Mathlib.Data.Multiset.Sym /-! # Symmetric powers of a finset This file defines the sym...
Additive.lean
/- Copyright (c) 2024 Sophie Morel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sophie Morel, Joël Riou -/ import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic /-! # Adjunctions between additive functors. This provides some results and constructions for adjuncti...
test_ssrAC.v
From mathcomp Require Import all_boot ssralg. Section Tests. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite orbACA. Abort. Lemma test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. Lemma ...
ToIntervalMod.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers -/ import Mathlib.Algebra.ModEq import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Ring.Periodic import Mathlib.Data.Int.SuccPred import Mathlib.Order.Cir...
test_rat.v
From mathcomp Require Import all_boot all_order all_algebra. Local Open Scope ring_scope. Goal 2%:Q + 2%:Q = 4%:Q. Proof. reflexivity. Qed. Goal - 2%:Q = -1 * 2%:Q. Proof. reflexivity. Qed. Goal 2%:Q ^+ 2 = 4%:Q. Proof. reflexivity. Qed. Goal (-1)^-1 = -1 :> rat. Proof. reflexivity. Qed. Local Open Scope rat_scop...
Lemmas.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Analysis.Normed.Field.Basic import Mathlib.Analysis.Normed.Group.Rat import Mathlib.Analysis.Normed.Ring.Lemmas import Mathlib.Topology...
PellMatiyasevic.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.Nat.ModEq import Mathlib.Data.Nat.Prime.Basic import Mathlib.NumberTheory.Zsqrtd.Basic /-! # Pell's equation and Matiyasevic's theorem This file...
RuzsaSzemeredi.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Combinatorics.Additive.AP.Three.Behrend import Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite import Mathlib.Tactic.Rify /-! # The Ruzsa-Szemerédi ...
FinPartOrd.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.CategoryTheory.FintypeCat import Mathlib.Order.Category.PartOrd /-! # The category of finite partial orders This defines `FinPartOrd`, the category of fi...
MultipleTransitivity.lean
/- Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Chambert-Loir -/ import Mathlib.GroupTheory.GroupAction.Primitive import Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup import Mathlib.SetTheory.Cardinal...
Basic.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Filippo A. E. Nuccio -/ import Mathlib.RingTheory.Localization.Integer import Mathlib.RingTheory.Localization.Submodule /-! # Fractional ideals This file defines fractional...
SumOverResidueClass.lean
/- Copyright (c) 2024 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.Analysis.Normed.Group.Basic import Mathlib.Data.ZMod.Basic import Mathlib.Topology.Instances.ENNReal.Lemmas /-! # Sums over residue classes We consider...
Hom.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.Group.Equiv.Defs import Mathlib.Algebra.Group.Hom.Basic import Mathlib.Algebra.Group.Nat.Defs import Mathlib.Algebra.Group.TypeTags.Hom impor...
Support.lean
/- Copyright (c) 2025 Yoh Tanimoto. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yoh Tanimoto -/ import Mathlib.Algebra.Order.Group.Indicator import Mathlib.Topology.Algebra.Support /-! # The topological support of sup and inf of functions In a topological space `X...
cyclotomic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
Defs.lean
/- Copyright (c) 2023 Koundinya Vajjha. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Koundinya Vajjha, Thomas Browning -/ import Mathlib.Data.Rat.Defs import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! This file defines the harmonic numbers. * `Mathilb/Num...
TautoSet.lean
/- Copyright (c) 2025 Lenny Taelman. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lenny Taelman -/ import Mathlib.Data.Set.SymmDiff import Mathlib.Data.Set.Disjoint /-! # The `tauto_set` tactic -/ assert_not_exists RelIso namespace Mathlib.Tactic.TautoSet open L...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
WithTop.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 -/ import Mathlib.Algebra.CharZero.Defs import Mathlib.Algebra.Group.Hom.Defs import Mathlib.Algebra.Order.Monoid.Unbund...
Pointwise.lean
/- Copyright (c) 2021 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Yaël Dillies -/ import Mathlib.Analysis.Normed.Group.Pointwise import Mathlib.Analysis.NormedSpace.Real /-! # Properties of pointwise scalar multiplication of se...
Basic.lean
/- Copyright (c) 2020 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.MeasureTheory.Measure.Content import Mathlib.MeasureTheory.Group.Prod import Mathlib.Topology.Algebra.Group.Compact /-! # Haar measure In this fi...
jordanholder.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype big...
Basic.lean
/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Leonardo de Moura, Mario Carneiro -/ import Lean.Linter.Deprecated import Mathlib.Data.Nat.Notation import Mathlib.Data.Int.Notation import Mathlib.Data.Nat.BinaryRec import Mat...
order.v
(* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import path fintype tup...
Orientation.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.LinearAlgebra.Ray import Mathlib.LinearAlgebra.Determinant /-! # Orientations of modules This file defines orientations of modules. ## Main definitions ...
finmodule.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...
SlashInvariantForms.lean
/- Copyright (c) 2022 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.NumberTheory.ModularForms.CongruenceSubgroups import Mathlib.NumberTheory.ModularForms.SlashActions /-! # Slash invariant forms This file defines fun...
Basic.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.Module.Projective import Mathlib.LinearAlgebra.Dimension.Finite import Mathlib.LinearAlgebra.FiniteDimensional.Defs /-! # Finite dimensional vecto...
Equivalence.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.Adjunction.Limits import Mathlib.CategoryTheory.Limits.Shapes.Terminal /-! # Transporting existence of specific limits across equivalence...
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, Bhavik Mehta -/ import Mathlib.CategoryTheory.Limits.Shapes.RegularMono import Mathlib.CategoryTheory.Limits.Shapes.Kernels import Mathlib.CategoryTheory.Limits.Preserves.B...
seq.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat. (******************************************************...
Point.lean
/- Copyright (c) 2025 David Kurniadi Angdinata. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Kurniadi Angdinata -/ import Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point import Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula /-! # Nonsingular poi...
Basic.lean
/- Copyright (c) 2025 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells import Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition /-! # Relative cell complexes In this f...
Basic.lean
/- Copyright (c) 2020 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Calle Sönne, Dagur Asgeirsson -/ import Mathlib.CategoryTheory.FintypeCat import Mathlib.Topology.Category.CompHaus.Basic import Mathlib.Topology.LocallyConstant.Basic im...
pnat_to_nat.lean
import Mathlib.Tactic.PNatToNat example (a b : PNat) (h : a < b) : 1 < b := by pnat_to_nat omega example (a b : PNat) (h : a = b) : b = a := by -- to test if the tactic works with inaccessible names let a : ℤ := 42 pnat_to_nat omega example (a b : PNat) (h : a < b) : 1 < b := by have := a.pos pnat_to...
ZMod.lean
/- Copyright (c) 2022 Alex J. Best. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best -/ import Mathlib.Algebra.Squarefree.Basic import Mathlib.Algebra.EuclideanDomain.Int import Mathlib.Data.ZMod.Basic import Mathlib.RingTheory.Nilpotent.Lemmas import Mathli...
Finsubgraph.lean
/- Copyright (c) 2022 Joanna Choules. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joanna Choules -/ import Mathlib.CategoryTheory.CofilteredSystem import Mathlib.Combinatorics.SimpleGraph.Subgraph /-! # Homomorphisms from finite subgraphs This file defines the typ...
Basic.lean
/- Copyright (c) 2023 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.Tactic.CategoryTheory.Bicategory.Basic /-! # Adjunctions in bicategories For 1-morphisms `f : a ⟶ b` and `g : b ⟶ a` in a bicategory, an adjunction between...
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.
Pochhammer.lean
/- Copyright (c) 2025 Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Horner -/ import Mathlib.Algebra.BigOperators.Field import Mathlib.Analysis.Convex.Deriv import Mathlib.Analysis.Convex.Piecewise import Mathlib.Data.Nat.Choose.Cast import M...
Pigeonhole.lean
/- Copyright (c) 2020 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller, Yury Kudryashov -/ import Mathlib.Algebra.Module.BigOperators import Mathlib.Algebra.Order.Ring.Nat import Mathlib.Data.Nat.ModEq import Mathlib.Order.Preorder.Finite /-! # ...
DomAct.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.MeasureTheory.Function.AEEqFun import Mathlib.MeasureTheory.Group.Action import Mathlib.GroupTheory.GroupAction.DomAct.Basic import Mathlib.MeasureTh...
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, Yury Kudryashov -/ import Mathlib.Data.Set.Defs import Mathlib.Tactic.TypeStar /-! # Definitions about upper/lower bounds In this file we define: * `upperBounds`, `lo...
ring_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 choice ssrnat. From mathcomp Require Import seq ssralg generic_q...
algebraics_fundamentals.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
Bell.lean
/- Copyright (c) 2024 Antoine Chambert-Loir & 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.Data.Nat.Choose.Multinomial import Mathlib.Data.Nat.Choose.Mul /-! # B...
all_fingroup.v
From mathcomp Require Export action. From mathcomp Require Export automorphism. From mathcomp Require Export fingroup. From mathcomp Require Export gproduct. From mathcomp Require Export morphism. From mathcomp Require Export perm. From mathcomp Require Export presentation. From mathcomp Require Export quotient.
FiniteType.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Harald Carlens, Andrew Yang, Jujian Zhang -/ import Mathlib.RingTheory.FiniteType import Mathlib.RingTheory.GradedAlgebra.Basic /-! # Graded algebras of finite type We s...
Pi.lean
/- Copyright (c) 2023 Yuyang Zhao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuyang Zhao -/ import Mathlib.Data.Multiset.Pi /-! # The cartesian product of lists ## Main definitions * `List.pi`: Cartesian product of lists indexed by a list. -/ namespace List n...
jordanholder.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq path. From mathcomp Require Import choice fintype big...
SetToL1.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Zhouhang Zhou, Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.FinMeasAdditive import Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness /-...
FunctorGamma.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.SimplicialObject.Split import Mathlib.AlgebraicTopology.DoldKan.PInfty /-! # Construction of the inverse functor of the Dold-Kan equivalence ...
StrictSegal.lean
/- Copyright (c) 2024 Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl, Joël Riou, Johan Commelin, Nick Ward -/ import Mathlib.AlgebraicTopology.SimplicialSet.Nerve import Mathlib.AlgebraicTopology.SimplicialSet.Path /-! # Strict...
Basic.lean
/- Copyright (c) 2019 Simon Hudon. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Simon Hudon -/ import Lean.Elab.Tactic.SolveByElim import Mathlib.Tactic.Monotonicity.Attr /-! # Monotonicity tactic The tactic `mono` applies monotonicity rules (collected through the ...
BaseChange.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.LinearAlgebra.Charpoly.ToMatrix import Mathlib.LinearAlgebra.Determinant import Mathlib.RingTheory.TensorProduct.Finite /-! # The characteristic polynomial...
Basic.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.Sites.Sheaf import Mathlib.Topology.Category.LightProfinite.EffectiveEpi /-! # Light condensed objects This file defines the categ...
TMToPartrec.lean
/- Copyright (c) 2020 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Computability.Halting import Mathlib.Computability.TuringMachine import Mathlib.Data.Num.Lemmas import Mathlib.Tactic.DeriveFintype import Mathlib.Comp...
QuotientGroup.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.Data.ZMod.Basic /-! # `ZMod n` and quotient groups / rings This file relates `ZMod n` to the quotient group `ℤ / AddSubgroup.zmultiples (n : ℤ)`. ## Main ...
Floor.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Kevin Kappelmann -/ import Mathlib.Algebra.Order.Round import Mathlib.Data.Rat.Cast.Order import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Ring /-...
WithTopBot.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Hom.BoundedLattice import Mathlib.Order.WithBot /-! # Adjoining `⊤` and `⊥` to order maps and lattice homomorphisms This file defines ways to adjoi...
ULift.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.Group.Equiv.Defs import Mathlib.Algebra.Group.InjSurj import Mathlib.Logic.Nontrivial.Basic /-! # `ULift` instances for groups and monoids This f...
CalculusOfFractions.lean
/- Copyright (c) 2023 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.Opposite /-! # Calculus of fractions Following the definitions by [Gabriel and Zisman][gabriel-zisman-1967], given a morphism prope...
StrictSegal.lean
/- Copyright (c) 2024 Nick Ward. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Emily Riehl, Nick Ward -/ import Mathlib.AlgebraicTopology.Quasicategory.Basic import Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal /-! # Strict Segal simplicial sets...
cyclotomic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
ConcreteSheafification.lean
/- Copyright (c) 2021 Adam Topaz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adam Topaz -/ import Mathlib.CategoryTheory.Sites.Plus import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory /-! # Sheafification We construct the sheafification of a presheaf ov...
SingleObj.lean
/- Copyright (c) 2022 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Bicategory.End import Mathlib.CategoryTheory.Monoidal.Functor /-! # Promoting a monoidal category to a single object bicategory. A monoida...
Curry.lean
/- Copyright (c) 2022 Kevin H. Wilson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin H. Wilson -/ import Mathlib.Order.Filter.Prod /-! # Curried Filters This file provides an operation (`Filter.curry`) on filters which provides the equivalence `∀ᶠ a in l, ∀ᶠ b...
TypeTags.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.Defs import Mathlib.Algebra.Group.TypeTags.Basic /-! # Additive and Multiplicative for group actions ## Tags group...
Transcendental.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.Data.Fin.Tuple.Reflection import Mathlib.RingTheory.Algebraic.MvPolynomial import Mathlib.RingTheory.AlgebraicIndependent.Basic /-! # Algebraic Independen...
hall.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 choice. From mathcomp Require Import fintype finset prime fingroup morphism. From ma...
Canonical.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.Sites.Sheaf /-! # The canonical topology on a category We define the finest (largest) Grothendieck topology for which a given presheaf `P`...
Full.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.CategoryTheory.Galois.Action /-! # Fiber functors are (faithfully) full Any (fiber) functor `F : C ⥤ FintypeCat` factors via the forgetful funct...
Indexes.lean
/- Copyright (c) 2020 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Mathlib.Util.AssertExists import Mathlib.Tactic.Cases import Mathlib.Data.List.Defs /-! # Lemmas about List.*Idx functions. Some specification lemmas for `Li...
Density.lean
/- Copyright (c) 2024 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.MapComap import Mathlib.Probability.Martingale.Convergence import Mathlib.Probability.Process.PartitionFiltration /-! # Ker...
fun_prop2.lean
import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.SpecialFunctions.Log.Deriv import Mathlib.MeasureTheory.MeasurableSpace.Basic import Mathlib.MeasureTheory.Measure.Haar.OfBasis noncomputable def foo (x : ℝ) := x * (Real.log x) ^ 2 - Real.exp x / x example : ContinuousOn foo {0}ᶜ := by unfol...
Subalgebra.lean
/- Copyright (c) 2024 Jz Pan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jz Pan -/ import Mathlib.LinearAlgebra.TensorProduct.Submodule import Mathlib.RingTheory.TensorProduct.Basic /-! # Some results on tensor product of subalgebras ## Linear maps induced by mu...
Random.lean
/- Copyright (c) 2022 Henrik Böving. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Henrik Böving -/ import Mathlib.Control.ULiftable import Mathlib.Order.Fin.Basic /-! # Rand Monad and Random Class This module provides tools for formulating computations guided by ra...
AffineEquiv.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.LinearAlgebra.AffineSpace.AffineMap import Mathlib.LinearAlgebra.GeneralLinearGroup /-! # Affine equivalences In this file we define `AffineEquiv k...
ZeroOne.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.Probability.Independence.Basic import Mathlib.Probability.Independence.Conditional /-! # Kolmogorov's 0-1 law Let `s : ι → MeasurableSpace Ω` be an indep...