filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Piecewise.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.ContinuousOn
/-!
### Continuity of piecewise defined functions
-/
open Set Filter Function Topology Filter
variable {α β : Type*} [Topologi... |
LocalRing.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.RingTheory.LocalRing.Module
import Mathlib.RingTheory.LocalRing.ResidueField.Ideal
import Mathlib.RingTheory.Unramified.Field
import Mathlib.RingTheory.Unram... |
MeanValue.lean | /-
Copyright (c) 2019 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.AffineMap
import Mathlib.Analysis.Calculus.Deriv.Comp
import Mathlib.Analysis.Calculus.Deriv.Mul
import Ma... |
Parity.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
-/
import Mathlib.Algebra.Ring.Parity
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Algebra.Group.Int.Even
/-!
# Basic parity lemmas for the ring `ℤ`
See note [fou... |
Pi.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.Algebra.BigOperators.Fin
import Mathlib.Logic.Encodable.Pi
import Mathlib.MeasureTheory.Group.Measure
import Mathlib.MeasureTheory.MeasurableSpace.... |
Basic.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang, Yury Kudryashov
-/
import Mathlib.Data.Fintype.Option
import Mathlib.Topology.Homeomorph.Lemmas
import Mathlib.Topology.Sets.Opens
/-!
# The OnePoint Compactification
We ... |
Biproducts.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.Algebra.Group.Pi.Lemmas
import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
import Mathlib.Algebra.Category.ModuleCat.Abelian
import Mathlib.Algeb... |
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... |
NormalForm.lean | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
import Mathlib.Analysis.Meromorphic.Divisor
/-!
# Normal form of meromorphic functions and continuous extension
If a function `f` is meromorphic on `U` and if `g` d... |
TypeTags.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.Order.Monoid.Unbundled.TypeTags
import Mathlib.Algebra.Order.Monoid.Canonical.Defs
/-! # Bund... |
Basic.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Yaël Dillies
-/
import Mathlib.Algebra.Group.Units.Basic
import Mathlib.Algebra.GroupWithZero.NeZero
import Mathlib.Algebra.Order.Group... |
Tight.lean | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Josha Dekker
-/
import Mathlib.MeasureTheory.Measure.RegularityCompacts
import Mathlib.Topology.Order.Lattice
/-!
# Tight sets of measures
A set of measures is tight if f... |
Opposite.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.RingTheory.Congruence.Basic
import Mathlib.GroupTheory.Congruence.Opposite
/-!
# Congruences on the opposite ring
This file defines the order isomorphism ... |
Order.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.Tactic.Order.CollectFacts
import Mathlib.Tactic.Order.Preprocessing
import Mathlib.Tactic.Order.Graph.Basic
import Mathlib.Tactic.Order.Graph.Tarja... |
MapLemmas.lean | /-
Copyright (c) 2023 Alex Keizer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Keizer
-/
import Mathlib.Data.Vector.Basic
import Mathlib.Data.Vector.Snoc
/-!
This file establishes a set of normalization lemmas for `map`/`mapAccumr` operations on vectors
-/
... |
Lemmas.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.Algebra.Group.TypeTags.Hom
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Algebra.Ring.Parity
/-!
# Cast of integers (additional theorems)
This ... |
Primal.lean | /-
Copyright (c) 2024 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.Algebra.Group.Submonoid.Defs
import Mathlib.Algebra.GroupWithZero.Divisibility
/-!
# Submonoid of primal elements
-/
assert_not_exists RelIso Ring
/-- The sub... |
OrdConnectedComponent.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.Order.Interval.Set.OrdConnected
import Mathlib.Data.Set.Lattice.Image
/-!
# Order connected components of a set
In this file we define `Set.ordConn... |
ssreflect.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From Corelib Require Export ssreflect.
Global Set SsrOldRewriteGoalsOrder.
Global Set Asymmetric Patterns.
Global Set Bullet Behavior "None".
#[deprecated(sinc... |
BddOrd.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.Category.Bipointed
import Mathlib.Order.Category.PartOrd
import Mathlib.Order.Hom.Bounded
/-!
# The category of bounded orders
This define... |
MGFAnalytic.lean | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Probability.Moments.ComplexMGF
import Mathlib.Analysis.SpecialFunctions.Complex.Analytic
import Mathlib.Analysis.Calculus.Taylor
/-!
# The moment generati... |
LieBracket.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.VectorField
import Mathlib.Geometry.Manifold.ContMDiffMFDeriv
import Mathlib.Geometry.Manifold.MFDeriv.NormedSpace
import Mathl... |
HomComplexShift.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.HomotopyCategory.HomComplex
import Mathlib.Algebra.Homology.HomotopyCategory.Shift
import Mathlib.Algebra.Module.Equiv.Basic
/-! Shifting cocha... |
Frontend.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yury Kudryashov, Floris van Doorn, Jon Eugster
-/
import Mathlib.Data.Nat.Notation
import Mathlib.Data.String.Defs
import Mathlib.Data.Array.Defs
import Mathlib.Lean.Ex... |
ContextFreeGrammar.lean | /-
Copyright (c) 2023 Martin Dvorak. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Dvorak
-/
import Mathlib.Computability.Language
/-!
# Context-Free Grammars
This file contains the definition of a context-free grammar, which is a grammar that has a single
no... |
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... |
Integrable.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Function.L1Space.Integrable
import Mathlib.Probability.Independence.Basic
/-!
# Independence of functions implies that the measure... |
Unramified.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.RingTheory.Unramified.Locus
import Mathlib.RingTheory.LocalProperties.Basic
/-!
# The meta properties of unramified ring homomorphisms.
-/
namespace Ring... |
Basic.lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Utensil Song
-/
import Mathlib.Algebra.RingQuot
import Mathlib.LinearAlgebra.TensorAlgebra.Basic
import Mathlib.LinearAlgebra.QuadraticForm.Isometry
import Mathlib.LinearAlge... |
Opposite.lean | /-
Copyright (c) 2024 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Opposite
/-!
# If `C` is braided, so is `Cᵒᵖ`.
Todo: we should also do `Cᵐᵒᵖ... |
Basic.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.Notation.Indicator
import Mathlib.Tactic.FinCases
import Mathlib.Topology.Connected.LocallyConnected
import Mathlib.Topology.Sets.Closeds
/-!
... |
Polynomial.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.Topology.Algebra.Polynomial
import Mathlib.Topology.ContinuousMap.Star
import Mathlib.Topology.UnitInterval
import Mathlib.Algebra.Star.Subalgebra
/-!
# C... |
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_... |
Dickson.lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import Mathlib.Algebra.CharP.Algebra
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Algebra.CharP.Lemmas
import Mathlib.Algebra.EuclideanDomain.Field
... |
Imo1964Q1.lean | /-
Copyright (c) 2020 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard
-/
import Mathlib.Tactic.IntervalCases
import Mathlib.Data.Nat.ModEq
import Mathlib.Tactic.Ring
/-!
# IMO 1964 Q1
(a) Find all positive integers $n$ for which $2^n-1$ is... |
NaturalOps.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
-/
import Mathlib.SetTheory.Ordinal.Family
import Mathlib.Tactic.Abel
import Mathlib.Tactic.Linter.DeprecatedModule
deprecated_module
"This mo... |
Explode.lean | import Mathlib.Tactic.Explode
import Mathlib.Data.Real.Basic
set_option linter.unusedVariables false
open Lean
/--
info: true_iff : ∀ (p : Prop), (True ↔ p) = p
0 │ │ p ├ Prop
1 │ │ x✝ │ ┌ True ↔ p
2 │ │ trivial │ │ True
3 │1,2 │ Iff.mp │ │ p
4 │1,3 │ ∀I │ (True ↔ p) → p
5 │ │... |
Basis.lean | /-
Copyright (c) 2020 Jalex Stark. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jalex Stark, Kim Morrison, Eric Wieser, Oliver Nash, Wen Yang
-/
import Mathlib.Data.Matrix.Basic
/-!
# Matrices with a single non-zero element.
This file provides `Matrix.single`. The ... |
Lattice.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
Kim Morrison
-/
import Mathlib.Data.List.Basic
/-!
# Lattice structure of lists
This files pro... |
UniformMulAction.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.Algebra.Module.Opposite
import Mathlib.Topology.UniformSpace.Completion
import Mathlib.Topology.Algebra.IsUniformGroup.Defs
/-!
# Multiplicative act... |
Union.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.Finset.Lattice.Fold
import Mathlib.Data.Finset.Union
/-!
# Relating `Finset.biUnion` with lattice operations
This file shows `Finset.biUnion` co... |
OpenImmersion.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.UnderlyingMap
/-!
# Open immersions
A morphism is an open immersion if the underlying map of spaces is an open embedding
`f : ... |
SubboxInduction.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.BoxIntegral.Box.SubboxInduction
import Mathlib.Analysis.BoxIntegral.Partition.Tagged
/-!
# Induction on subboxes
In this file we prove (se... |
SuccAboveOrderIso.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.Order.Fin.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Tactic.FinCases
/-!
# The order isomorphism `Fin (n + 1) ≃o {i}ᶜ`
Given `i : Fin (n + 2)`, we... |
Lemmas.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import Mathlib.Logic.Equiv.Fin.Basic
import Mathlib.Topology.Connected.LocallyConnected
import Mathlib.Top... |
Classifier.lean | /-
Copyright (c) 2024 Charlie Conneen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Charlie Conneen, Pablo Donato, Klaus Gy
-/
import Mathlib.CategoryTheory.Limits.Shapes.RegularMono
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryT... |
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, Junyan Xu, Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Liouville
import Mathlib.Analysis.Calculus.Deriv.Polynomial
import Mathlib.Data.Complex.FiniteDimensional
impo... |
gproduct.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... |
Algebraic.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
import Mathlib.FieldTheory.IntermediateField.Basic
import Mathlib.FieldTheory.Minpoly.Basic
import Mathlib.FieldTheory.Tower
import Mathlib.LinearAlgebra.FreeModule.StrongR... |
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... |
YoungDiagram.lean | /-
Copyright (c) 2022 Jake Levinson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jake Levinson
-/
import Mathlib.Data.Finset.Preimage
import Mathlib.Data.Finset.Prod
import Mathlib.Data.SetLike.Basic
import Mathlib.Order.UpperLower.Basic
/-!
# Young diagrams
A You... |
Imo2001Q2.lean | /-
Copyright (c) 2021 Tian Chen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tian Chen
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# IMO 2001 Q2
Let $a$, $b$, $c$ be positive reals. Prove that
$$
\frac{a}{\sqrt{a^2 + 8bc}} +
\frac{b}{\sqrt{b^2 + 8ca}}... |
Sym.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.Data.Finset.Sym
import Mathlib.Data.Sym.Sym2.Order
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Lemmas on `Finset.sum` and `Finset.prod` inv... |
Lookmap.lean | /-
Copyright (c) 2014 Parikshit Khanna. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
import Batteries.Logic
import Batteries.Data.List.Basic
import Mathlib.Tactic.TypeStar
/-! ##... |
PathComponentOne.lean | /-
Copyright (c) 2025 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Topology.Algebra.OpenSubgroup
import Mathlib.Topology.Connected.LocPathConnected
/-! # The path component of the identity in a locally path connected to... |
Interval.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.Order.Interval.Set.OrdConnected
import Mathlib.Order.Filter.SmallSets
import Mathlib.Order.Filter.AtTopBot.Basic
import Mathlib.Order.Filter.Bases.Fi... |
Covering.lean | /-
Copyright (c) 2022 Antoine Labelle, Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Labelle, Rémi Bottinelli
-/
import Mathlib.Combinatorics.Quiver.Cast
import Mathlib.Combinatorics.Quiver.Symmetric
import Mathlib.Data.Sigma.Basic
import Math... |
Statement.lean | /-
Copyright (c) 2023 Lean FRO LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
/-!
# If normalization
Rustan Leino, Stephan Merz, and Natarajan Shankar have recently been discussing challenge problems
to compare proof assistants.
(See https://lean... |
Lemmas.lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes Hölzl, Kim Morrison, Jens Wagemaker
-/
import Mathlib.Algebra.Polynomial.Eval.Degree
import Mathlib.Algebra.Prime.Lemmas
/-!
# Theory of degrees of polynomials
S... |
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... |
Solid.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.Functor.KanExtension.Pointwise
import Mathlib.Condensed.Functors
import Mathlib.Condensed.Limits
/-!
# Solid modules
This file co... |
StronglyMeasurable.lean | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
import Mathlib.MeasureTheory.Constructions.Polish.Basic
import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
/-!
# Results about strongly measurable functi... |
Deriv.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
-/
import Mathlib.Analysis.Calculus.Deriv.Pow
import Mathlib.Analysis.Calculus.LogDeriv
import Mathlib.Analysis.SpecialFuncti... |
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... |
Bounds.lean | /-
Copyright (c) 2025 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.Unbundled.Basic
import Mathlib.Order.Bounds.Basic
import Mathlib.Order.Bounds.Image
/-!
#... |
Polynomial.lean | /-
Copyright (c) 2025 Jingting Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jingting Wang
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.RingTheory.KrullDimension.PID
import Mathlib.RingTheory.LocalRing.ResidueField.Fiber
/-!
# Krull dimensi... |
Finite.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison
-/
import Mathlib.Algebra.Module.Torsion
import Mathlib.LinearAlgebra.Dimension.Finite
/-!
# Results relating rank and tors... |
Ordnode.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.Order.Compare
import Mathlib.Data.List.Defs
import Mathlib.Data.Nat.PSub
import Mathlib.Data.Option.Basic
/-!
# Ordered sets
This file defines a data... |
TFAE.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.RingTheory.DedekindDomain.Basic
import Mathlib.RingTheory.DiscreteValuationRing.Basic
import Mathlib.RingTheory.Finiteness.Ideal
import Mathlib.RingTheory.Id... |
Kernels.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.Limits.Shapes.Kernels
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero
/-!
# Preserving (co)kernels
Constructions to relate the ... |
BigOperators.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.Algebra.BigOperators.WithTop
import Mathlib.Data.NNReal.Basic
import Mathlib.Data.ENNReal.Inv
/-!
# Properties of big operators exten... |
Opposite.lean | /-
Copyright (c) 2024 Daniel Carranza. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Carranza
-/
import Mathlib.CategoryTheory.Enriched.Ordinary.Basic
import Mathlib.CategoryTheory.Monoidal.Braided.Basic
/-!
# The opposite category of an enriched category
Wh... |
Maps.lean | /-
Copyright (c) 2021 Hunter Monroe. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hunter Monroe, Kyle Miller
-/
import Mathlib.Combinatorics.SimpleGraph.Dart
import Mathlib.Data.FunLike.Fintype
import Mathlib.Logic.Embedding.Set
/-!
# Maps between graphs
This file ... |
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... |
Period.lean | /-
Copyright (c) 2024 Emilie Burgun. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Emilie Burgun
-/
import Mathlib.Dynamics.PeriodicPts.Lemmas
import Mathlib.GroupTheory.Exponent
import Mathlib.GroupTheory.GroupAction.Basic
/-!
# Period of a group action
This modul... |
CondexpL2.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Basic
import Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique
import Mathlib.MeasureTheory.Function.L2Spa... |
tfae.lean | import Mathlib.Tactic.TFAE
import Mathlib.Tactic.SuccessIfFailWithMsg
open List
set_option autoImplicit true
section zeroOne
example : TFAE [] := by tfae_finish
example : TFAE [P] := by tfae_finish
end zeroOne
namespace two
axiom P : Prop
axiom Q : Prop
axiom pq : P → Q
axiom qp : Q → P
example : TFAE [P, Q] :=... |
Algebra.lean | /-
Copyright (c) 2025 Christian Merten, Yi Song, Sihan Su. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten, Yi Song, Sihan Su
-/
import Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
import Mathlib.RingTheory.Ideal.Over
import Mathlib.RingTheory.LocalRing... |
RamificationGroup.lean | /-
Copyright (c) 2022 Michail Karatarakis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michail Karatarakis
-/
import Mathlib.RingTheory.LocalRing.ResidueField.Basic
import Mathlib.RingTheory.Valuation.ValuationSubring
/-!
# Ramification groups
The decomposition su... |
Sphere.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.Analysis.Calculus.Deriv.Inv
import Mathlib.Analysis.Complex.Circle
import Mathlib.Analysis.NormedSpace.BallAction
import Mathlib.Analysis.SpecialFunc... |
GaloisObjects.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.Limits.FintypeCat
import Mathlib.CategoryTheory.Limits.Preserves.Limits
import Mathlib.Ca... |
FunctorExtension.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.CategoryTheory.Idempotents.Karoubi
/-!
# Extension of functors to the idempotent completion
In this file, we construct an extension `functorExtension₁`
of func... |
eqtype.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.
(********************************************************************... |
HomologicalComplex.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.Additive
import Mathlib.Algebra.Homology.ShortComplex.Exact
import Mathlib.Algebra.Homology.ShortComplex.Preadditive
import Mathlib.Tactic.Linar... |
Imo2013Q5.lean | /-
Copyright (c) 2021 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Ring.GeomSum
import Mathlib.Algebra.Ring.Regular
import Mathlib.Data.Real.Archimedean
impo... |
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.... |
HarrisKleitman.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.Algebra.Order.Ring.Canonical
import Mathlib.Algebra.Order.Ring.Nat
import Mathlib.Combinatorics.SetFamily.Compression.Down
import Mathlib.Data.Fintype.Powe... |
Localization.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.Localization.Bousfield
import Mathlib.CategoryTheory.Sites.Sheafification
/-!
# The sheaf category as a localized category
In this file, it is s... |
alt.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 choice.
From mathcomp Require Import div fintype tupl... |
mxpoly.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 div fintype tupl... |
RingEquiv.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.Ring.Equiv
import Mathlib.Algebra.Ring.Opposite
import Mathlib.Algebra.BigOperators.Group.Finset.Defs
/-!
# Re... |
EpiMono.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.Constructions.EpiMono
import Mathlib.CategoryTheory.Limits.FunctorCategory.Basic
/-!
# Monomorphisms and epimorphisms in functor categorie... |
Semiconj.lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.Algebra.Group.Semiconj.Units
/-!
# Lemmas about semiconjugate elements in a `GroupWithZero`.
-/
ass... |
InferParam.lean | import Mathlib.Tactic.InferParam
namespace InferParamTest
theorem zero_le_add (a : Nat) (ha : 0 ≤ a := Nat.zero_le a) : 0 ≤ a + a := calc
0 ≤ a := ha
_ ≤ a + a := Nat.le_add_left _ _
theorem zero_le_add' (a : Nat) (ha : 0 ≤ a := by decide) : 0 ≤ a + a := zero_le_add a ha
example : 0 ≤ 2 + 2 := by
fail_if_succ... |
Copy.lean | /-
Copyright (c) 2023 Yaël Dillies, Mitchell Horner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Mitchell Horner
-/
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Combinatorics.SimpleGraph.Subgraph
/-!
# Containment of graphs
This file introdu... |
Grothendieck.lean | /-
Copyright (c) 2020 Bhavik Mehta, Edward Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Edward Ayers
-/
import Mathlib.CategoryTheory.Sites.Sieves
import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
import Mathlib.CategoryTheory.Category.P... |
BoolIndicator.lean | /-
Copyright (c) 2022 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson, Leonardo de Moura
-/
import Mathlib.Order.BooleanAlgebra.Set
/-!
# Indicator function valued in bool
See also `Set.indicator` and `Set.piecewise`.
-/
assert_not_... |
div.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.
(******************************************************************************)
(* Th... |
Grade.lean | /-
Copyright (c) 2022 Yaël Dillies, Violeta Hernández Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Violeta Hernández Palacios, Grayson Burton, Vladimir Ivanov
-/
import Mathlib.Data.Int.SuccPred
import Mathlib.Order.Fin.Basic
/-!
# Graded ord... |
Sensitivity.lean | /-
Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Michael Han, Chris Hughes, Robert Y. Lewis,
Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Jesse Michael Han, Chris Hughes, Robert Y. Lewis,
Patrick Massot
-/
import... |
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