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IsFundamentalgroup.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.Basic import Mathlib.CategoryTheory.Galois.Topology import Mathlib.CategoryTheory.Galois.Prorepresentability import Mathlib.T...
Int.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.Data.Int.Interval import Mathlib.Data.Int.ConditionallyCompleteOrder import Mathlib.Topology.Instances.Discrete import Mathlib.Topology...
FrobeniusFractionField.lean
/- Copyright (c) 2022 Robert Y. Lewis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Robert Y. Lewis, Heather Macbeth -/ import Mathlib.Data.Nat.Cast.WithTop import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.RingTheory.WittVector.DiscreteValuationRing /-! #...
convert.lean
import Mathlib.Tactic.Convert import Mathlib.Algebra.Group.Basic import Mathlib.Data.Set.Image private axiom test_sorry : ∀ {α}, α set_option autoImplicit true namespace Tests example (P : Prop) (h : P) : P := by convert h example (α β : Type) (h : α = β) (b : β) : α := by convert b example (α β : Type) (h : ∀ α...
Rank.lean
/- Copyright (c) 2024 Dexin Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dexin Zhang -/ import Mathlib.Logic.UnivLE import Mathlib.SetTheory.Ordinal.Rank import Mathlib.SetTheory.ZFC.Basic /-! # Ordinal ranks of PSet and ZFSet In this file, we define the ord...
integral_char.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...
Prod.lean
/- Copyright (c) 2024 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.Order.Star.Basic import Mathlib.Algebra.Star.Prod import Mathlib.Algebra.Ring.Prod /-! # Products of star-ordered rings -/ variable {α β : Type*} ...
Const.lean
/- Copyright (c) 2019 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Sébastien Gouëzel, Yury Kudryashov -/ import Mathlib.Analysis.Calculus.FDeriv.Congr /-! # Fréchet derivative of constant functions This file contains the usual formulas...
EnoughInjectives.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.Homology.DerivedCategory.Ext.ExactSequences /-! # Smallness of Ext-groups from the existence of enough injectives Let `C : Type u` be an abelian catego...
BigOperators.lean
/- Copyright (c) 2023 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Floris van Doorn -/ import Mathlib.Tactic.NormNum.Basic import Mathlib.Data.List.FinRange import Mathlib.Algebra.BigOperators.Group.Finset.Basic /-! # `norm_num` plugin for ...
fieldext.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 tupl...
Submodule.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.RingTheory.Localization.FractionRing import Mathlib.RingTheory.Localization.Ideal import Mathlib....
BigOperators.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 -/ import Mathlib.Data.Rat.Cast.CharZero import Mathlib.Algebra.BigOperators.Group.Finset.Defs /-! # Casting lemmas for rational numbers involving sums ...
AreComplementary.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.Homology.Embedding.TruncLEHomology /-! # Complementary embeddings Given two embeddings `e₁ : c₁.Embedding c` and `e₂ : c₂.Embedding c` of complex shape...
Basic.lean
/- Copyright (c) 2022 Joseph Myers. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joseph Myers, Heather Macbeth -/ import Mathlib.Analysis.InnerProductSpace.TwoDim import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic /-! # Oriented angles. This file defines orie...
BooleanAlgebra.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.Basic import Mathlib.Data.Finset.Image import Mathlib.Data.Fintype.Defs /-! # `Finset`s are a boolean algebra This file provides the `Boo...
Noetherian.lean
/- Copyright (c) 2024 Geno Racklin Asher. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Geno Racklin Asher -/ import Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated import Mathlib.RingTheory.Localization.Submodule import Mathlib.RingTheory.Spectrum.Prime.Noetherian...
IntegrationByParts.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Patrick Massot, Sébastien Gouëzel -/ import Mathlib.Analysis.Calculus.Deriv.Mul import Mathlib.Analysis.Calculus.Deriv.Slope import Mathlib.MeasureTheory.Integral.Int...
rat.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 prime fintype fi...
Equiv.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov -/ import Mathlib.Algebra.Group.Units.Equiv import Mathlib.Algebra.GroupWithZero.Units.Basic /-! # Multiplication by a nonzero element i...
HilbertCubeEmbedding.lean
/- Copyright (c) 2025 Vasilii Nesterov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Vasilii Nesterov -/ import Mathlib.Topology.UnitInterval /-! # Every compact metric space can be embedded into the Hilbert cube. In this file we prove `exists_closed_embedding_to_h...
EquivalenceGroupAddGroup.lean
/- Copyright (c) 2022 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.Algebra.Category.Grp.Basic /-! # Equivalence between `Group` and `AddGroup` This file contains two equivalences: * `groupAddGroupEquivalence` : the equiv...
TransfiniteCompositionLifting.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.SmallObject.WellOrderInductionData import Mathlib.CategoryTheory.MorphismProperty.LiftingProperty import Mathlib.CategoryTheory.MorphismProperty.T...
Core.lean
/- Copyright (c) 2023 Mario Carneiro, Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Heather Macbeth, Jovan Gerbscheid -/ import Lean import Batteries.Lean.Except import Batteries.Tactic.Exact import Mathlib.Lean.Elab.Term import Mathli...
Order.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, Floris van Doorn -/ import Mathlib.Algebra.Order.GroupWithZero.Canonical import Mathlib.Algebra.Order.Ring.Canonical import Mathlib.Data.Fintype.Option ...
SetIsMax.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.Order.Max import Mathlib.Data.Set.CoeSort /-! # Maximal elements of subsets Let `S : Set J` and `m : S`. If `m` is not a maximal element of `S`, then `↑m : J` ...
Pretriangulated.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.Triangulated.Opposite.Triangle import Mathlib.CategoryTheory.Triangulated.HomologicalFunctor /-! # The (pre)triangulated structure on the opposit...
FunctionField.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Ashvni Narayanan -/ import Mathlib.FieldTheory.RatFunc.Degree import Mathlib.RingTheory.DedekindDomain.IntegralClosure import Mathlib.RingTheory.IntegralClosure.IntegrallyClo...
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.ULift import Mathlib.Algebra.GroupWithZero.InjSurj /-! # `ULift` instances for groups and monoids with zero This file defines instances for...
LinearPMap.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Moritz Doll -/ import Mathlib.LinearAlgebra.Prod /-! # Partially defined linear maps A `LinearPMap R E F` or `E →ₗ.[R] F` is a linear map from a submodule of `E` to...
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...
TopologistsSineCurve.lean
/- Copyright (c) 2025 Daniele Bolla. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Daniele Bolla, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse import Mathlib.Topology.Connected.PathConnected /-! # The "topologist's sine curve" is c...
Inv.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.ENNReal.Operations /-! # Results about division in extended non-negative reals This file establishes basic properties related t...
MemPartition.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.Data.Set.Finite.Lattice /-! # Partitions based on membership of a sequence of sets Let `f : ℕ → Set α` be a sequence of sets. For `n : ℕ`, we can form th...
Basic.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Simon Hudon, Mario Carneiro -/ import Aesop import Mathlib.Algebra.Group.Defs import Mathlib.Data.Int.Init import Mathlib.Logic.Function.Iterate import...
Basic.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Yaël Dillies -/ import Mathlib.Order.Cover import Mathlib.Order.Interval.Finset.Defs import Mathlib.Order.Preorder.Finite /-! # Intervals as finsets This file provides ba...
Metrizable.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.Normed.Module.FiniteDimension import Mathlib.Geometry.Manifold.IsManifold.Basic import Mathlib.Topology.Compactness.Paracompact import Mathl...
Basic.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.Limits.Final import Mathlib.CategoryTheory.Functor.TwoSquare /-! # Guitart exact squares Given four functors `T`, `L`, `R` and `B`, a 2-square `...
Side.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.Analysis.Convex.Between import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Analysis.Normed.Module.Convex /-! # Sides of affine subspaces This ...
EReal.lean
/- Copyright (c) 2019 Kevin Buzzard. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard -/ import Mathlib.Data.EReal.Basic deprecated_module (since := "2025-04-13")
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...
Congr.lean
/- Copyright (c) 2025 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.SimpleRing.Basic import Mathlib.RingTheory.TwoSidedIdeal.Operations /-! # Simpleness is preserved by ring isomorphism/surjective ring homomorp...
ClosedSubgroup.lean
import Mathlib.Topology.Algebra.Group.ClosedSubgroup deprecated_module (since := "2025-04-21")
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...
TrivSqZeroExt.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Eric Wieser -/ import Mathlib.Algebra.BigOperators.GroupWithZero.Action import Mathlib.Algebra.GroupWithZero.Invertible import Mathlib.LinearAlgebra.Prod import Mathlib.Algebra.A...
Defs.lean
/- Copyright (c) 2022 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Yuyang Zhao -/ import Mathlib.Algebra.Order.Monoid.Unbundled.Defs import Mathlib.Tactic.MkIffOfInductiveProp import Mathlib.Util.Notation3 /-! # (Strict) monotonicity of...
Isometry.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Algebra.CharP.Invertible import Mathlib.Analysis.Normed.Operator.LinearIsometry import Mathlib.Analysis.Normed.Group.AddTorsor import Mathlib.Analysi...
Three.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca, Pietro Monticone -/ import Mathlib.NumberTheory.Cyclotomic.Embeddings import Mathlib.NumberTheory.Cyclotomic.Rat import Mathlib.NumberTheory.NumberField.Units.Dirich...
perm.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 tup...
Compact.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, Patrick Massot -/ import Mathlib.Topology.UniformSpace.Basic import Mathlib.Topology.Compactness.Compact /-! # Compact sets in uniform spaces * `compa...
Nilpotent.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.RingTheory.Ideal.Quotient.Operations import Mathlib.RingTheory.Nilpotent.Lemmas /-! # Nilpotent elements in quotient rings -/ theorem Ideal.isRadical_iff_q...
ToTensorPower.lean
/- Copyright (c) 2021 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.TensorAlgebra.Basic import Mathlib.LinearAlgebra.TensorPower.Basic /-! # Tensor algebras as direct sums of tensor powers In this file we show...
Leibniz.lean
/- Copyright (c) 2020 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson, Jeremy Tan -/ import Mathlib.Analysis.Complex.AbelLimit import Mathlib.Analysis.SpecialFunctions.Complex.Arctan /-! ### Leibniz's series for `π` -/ namespace Re...
Archimedean.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Floris van Doorn -/ import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Order.Group.Pointwise.Bounds import Mathlib.Data.Real.Basic import Mathlib.Ord...
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
fintype.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 ssrnotations eqtype. From mathcomp Require Import ssrnat seq choice pat...
FaaDiBruno.lean
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.IteratedDeriv.Defs /-! # Iterated derivatives of compositions In this file we spe...
PrimitiveElement.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.Data.Fintype.Pigeonhole import Mathlib.FieldTheory.IsAlgClosed.Basic import Mathlib.FieldTheory.SplittingField.Constructi...
all_algebra.v
(* N.B. interval_inference is not exported here. To enjoys the automation it provides, you need to explictly "Import interval_inference". *) From mathcomp Require Export ssralg. From mathcomp Require Export ssrnum. From mathcomp Require Export finalg. From mathcomp Require Export countalg. From mathcomp Require Export...
InnerDual.lean
/- Copyright (c) 2021 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Yaël Dillies -/ import Mathlib.Analysis.Convex.Cone.Dual import Mathlib.Analysis.InnerProductSpace.Adjoint /-! # Inner dual cone of a set We define the inner ...
Defs.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.List.Perm.Subperm import Mathlib.Data.Quot import Mathlib.Order.Monotone.Defs import Mathlib.Order.RelClasses import Mathlib.Tactic.Monoton...
Trunc.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Kenny Lau -/ import Mathlib.Algebra.Polynomial.Coeff import Mathlib.Algebra.Polynomial.Degree.Lemmas import Mathlib.RingTheory.PowerSeries.Basic /-! # Formal power se...
closed_field.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import fintype generic_...
UnusedTactic.lean
import Mathlib.Tactic.Linter.UnusedTactic import Mathlib.Tactic.AdaptationNote example (h : 0 + 1 = 0) : False := by change 1 = 0 at h simp at h example : 0 + 1 = 1 := by change 1 = 1 rfl /-- warning: 'change 1 = 1' tactic does nothing Note: This linter can be disabled with `set_option linter.unusedTactic f...
OrdConnectedLinear.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Buzzard, Bhavik Mehta, Oliver Nash -/ import Mathlib.Data.Nat.Lattice import Mathlib.Data.Int.ConditionallyCompleteOrder import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Suc...
Defs.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.Algebra.Polynomial.Basic import Mathlib.Algebra.Ring.NonZeroDivisors import Mathlib.RingTheory.Localization.FractionRing /-! # The field of rational functio...
IsNormal.lean
/- Copyright (c) 2025 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.SuccPred.InitialSeg /-! # Normal functions A normal function between well-orders is a strictly monotonic continuous fun...
Defs.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Kevin Kappelmann -/ import Mathlib.Tactic.Positivity.Core /-! # Floor and ceil We define the natural- and integer-valued floor and ceil functions on linearly ordered ...
Completion.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.Topology.UniformSpace.AbstractCompletion /-! # Hausdorff completions of uniform spaces The goal is to construct a left-adjoint to the...
FundamentalGroup.lean
/- Copyright (c) 2021 Mark Lavrentyev. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mark Lavrentyev -/ import Mathlib.CategoryTheory.Groupoid import Mathlib.Topology.Category.TopCat.Basic import Mathlib.Topology.Connected.PathConnected import Mathlib.Topology.Homotop...
PiInduction.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.Data.Finset.Max import Mathlib.Data.Finset.Sigma import Mathlib.Data.Fintype.Basic /-! # Induction principles for `∀ i, Finset (α i)` In this file ...
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 -/ import Mathlib.CategoryTheory.Abelian.Basic import Mathlib.CategoryTheory.Preadditive.Opposite import Mathlib.CategoryTheory.Limits.Opposites /-! # The opposite of an ab...
CondCDF.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym import Mathlib.MeasureTheory.Measure.Prod import Mathlib.Probability.Kernel.Disintegration.CDFToKernel /-...
all_boot.v
Require Export ssreflect. Require Export ssrbool. Require Export ssrfun. Require Export eqtype. Require Export ssrnat. Require Export seq. Require Export choice. Require Export monoid. Require Export nmodule. Require Export path. Require Export div. Require Export fintype. Require Export fingraph. Require Export tuple....
Basic.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Category.Grp.Abelian import Mathlib.Algebra.Category.Grp.Adjunctions import Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic import Mathlib.CategoryThe...
fun_prop_dev.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.Tactic.FunProp import Mathlib.Logic.Function.Basic import Mathlib.Data.FunLike.Basic import Mathlib.Tactic.SuccessIfFailWithMsg import Aesop /-! # Tests...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
finset.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 div seq. From mathcomp Require Import choice fintype finf...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Johannes Hölzl, Yury Kudryashov, Patrick Massot -/ import Mathlib.Algebra.Field.GeomSum import Mathlib.Order.Filter.AtTopBot.Archimedean import Mathlib.Order.Iterate...
AdicValuation.lean
/- Copyright (c) 2022 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.Ring.IsNonarchimedean import Mathlib.Data.Int.WithZero import Mathlib.RingTheory.DedekindDomain.Ideal.Lem...
lpSpace.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.CStarAlgebra.Classes import Mathlib.Analysis.Normed.Lp.lpSpace /-! # `lp ∞ A` as a C⋆-algebra We place these here because, for reasons related...
LagrangeMultipliers.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.Analysis.Calculus.FDeriv.Prod import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv import Mathlib.LinearAlgebra.Dual.Defs /-! # Lagrange m...
PowMod.lean
/- Copyright (c) 2023 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.Tactic.NormNum.Pow /-! # `norm_num` handling for expressions of the form `a ^ b % m`. These expressions can often be evaluated efficiently in cases whe...
vcharacter.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...
Complex.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, Benjamin Davidson -/ import Mathlib.Algebra.QuadraticDiscriminant import Mathlib.Analysis.SpecialFunctions.Pow.Complex /-! ...
Hom.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Kevin Buzzard, Kim Morrison, Johan Commelin, Chris Hughes, Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Algebra.Group.Commute.Defs import Mathlib.Algebra.Group.H...
Opposites.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.Defs import Mathlib.Logic.Equiv.Defs import Mathlib.Logic.Nontrivial.Basic import Mathlib.Logic.IsEmpty /-! # Multiplicative opposite and algebrai...
Multigoal.lean
import Mathlib.Tactic.Basic import Mathlib.Tactic.Conv import Mathlib.Tactic.Linter.Multigoal import Mathlib.Util.SleepHeartbeats import Mathlib.Tactic.SuccessIfFailWithMsg set_option linter.style.multiGoal true -- A deactivated linter does nothing. set_option linter.style.multiGoal false in example : True := by by...
Equalizer.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.RingTheory.Flat.Basic /-! # Base change along flat modules preserves equalizers We show that base change along flat modules (resp. algebras) pres...
all.v
From mathcomp Require Export all_boot. From mathcomp Require Export all_order. From mathcomp Require Export all_fingroup. From mathcomp Require Export all_algebra. From mathcomp Require Export all_solvable. From mathcomp Require Export all_field. From mathcomp Require Export all_character.
UniversallyOpen.lean
/- Copyright (c) 2025 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation import Mathlib.AlgebraicGeometry.Morphisms.Flat import Mathlib.AlgebraicGeometry.Morphisms.Underlyin...
Countable.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.Limits.Final import Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts import Mathlib.CategoryTheory.Countable import Mathlib.Data....
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 ...
Sum.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.Sum import Mathlib.Data.Fintype.EquivFin import Mathlib.Logic.Embedding.Set /-! ## Instances We provide the `Fintype` instance for the su...
Tendsto.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jeremy Avigad, Yury Kudryashov, Patrick Massot -/ import Mathlib.Order.Filter.AtTopBot.Disjoint import Mathlib.Order.Filter.Tendsto /-! # Limits of `Filter.atTop` and ...
Finset.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.Data.Finset.Fold import Mathlib.Algebra.GCDMonoid.Multiset /-! # GCD and LCM operations on finsets ## Main definitions - `Finset.gcd` - the greatest...
perm.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 tup...
Cartesian.lean
/- Copyright (c) 2024 Calle Sönne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Lezeau, Calle Sönne -/ import Mathlib.CategoryTheory.FiberedCategory.HomLift /-! # Cartesian morphisms This file defines cartesian resp. strongly cartesian morphisms with respect ...
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: ...
TeichmullerTukey.lean
/- Copyright (c) 2025 Ansar Azhdarov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ansar Azhdarov -/ import Mathlib.Data.Set.Finite.Range import Mathlib.Data.Set.Finite.Lattice import Mathlib.Order.Zorn /-! # Teichmuller-Tukey This file defines the notion of being ...