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Lean.lean
/- Copyright (c) 2025 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster, Arthur Paulino -/ import Lean.Data.Json import Lean.Util.Path /-! # Helper Functions This file contains helper functions that could potentially be upstreamed to Lean or re...
Defs.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad -/ import Mathlib.Algebra.CharZero.Defs import Mathlib.Algebra.Ring.Defs import Mathlib.Algebra.Group.Int.Defs import Mathlib.Data.Int.Cast.Basic import Mathlib.Algebra.Ri...
Basic.lean
/- Copyright (c) 2021 Aaron Anderson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Aaron Anderson, Michael Stoll -/ import Mathlib.Analysis.PSeries import Mathlib.Analysis.Normed.Module.FiniteDimension import Mathlib.Data.Complex.FiniteDimensional /-! # L-series Gi...
preorder.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...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
Density.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym import Mathlib.MeasureTheory.Measure.Haar.OfBasis import Mathlib.Probability.Independence.Basic /-! # Proba...
ZeroLimit.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.LinearAlgebra.LinearIndependent.Basic import Mathlib.Topology.Category.Profinite.Nobeling.Basic /-! # The zero and limit cases in the induction fo...
nilpotent.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 fintype div bigop prime finset fingroup morphism. Fro...
archimedean.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 fintype bigop or...
UnivLE.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Logic.UnivLE import Mathlib.CategoryTheory.EssentialImage import Mathlib.CategoryTheory.Types /-! # Universe inequalities and essential surjectivity of `u...
Span.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.LinearAlgebra.Finsupp.Defs import Mathlib.LinearAlgebra.Span.Basic /-! # Finitely supported functions and spans ## Tags function with finite support...
fingraph.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. From mathcomp Require Import seq path fintype. (******************************************...
Dissociation.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise import Mathlib.Algebra.Group.Pointwise.Set.Basic import Mathlib.Algebra.Group.Units.Equiv import Mathlib.Algebr...
Option.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.Data.Finsupp.Basic import Mathlib.Algebra.Module.Defs /-! # Declarations about finitely supported functions whose support is an `Option` type p ## Main d...
AddCircle.lean
/- Copyright (c) 2021 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth, David Loeffler -/ import Mathlib.Analysis.SpecialFunctions.ExpDeriv import Mathlib.Analysis.SpecialFunctions.Complex.Circle import Mathlib.Analysis.InnerProductSpace....
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.Ring.Equiv import Mathlib.Data.Int.Cast.Basic /-! # `ULift` instances for ring This file defines instances for...
Instances.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.Control.EquivFunctor import Mathlib.Data.Fintype.OfMap /-! # `EquivFunctor` instances We derive some `EquivFunctor` instances, to enable `equiv_rw` to re...
Relation.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Logic.Relator import Mathlib.Tactic.Use import Mathlib.Tactic.MkIffOfInductiveProp import Mathlib.Tactic.SimpRw import Mathlib.Logic.Basic import Mathl...
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...
Stopping.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.Probability.Process.Adapted import Mathlib.MeasureTheory.Constructions.BorelSpace.Order /-! # Stopping times, stopped processes and stopped va...
Chebyshev.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.Data.Complex.Trigonometric import Mathlib.Data.Complex.Module import Mathlib.RingTheory.Polynomial.Chebyshev /-! # Multiple angle formulas in terms of...
monoid.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype choice ssrnat seq. From mathcomp Require Import bigop fintype finfun. (******************************************************************************) (* Group-like structures ...
BigOperators.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.Data.List.MinMax import Mathlib.Algebra.Tropical.Basic import Mathlib.Order.ConditionallyCompleteLattice.Finset import Mathlib.Algebra.BigOperators.G...
BinaryProducts.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.Limits.Shapes.BinaryProducts import Mathlib.CategoryTheory.Limits.Preserves.Basic /-! # Preserving binary products Constructions to relate...
FormalCoproducts.lean
/- Copyright (c) 2025 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Kenny Lau -/ import Mathlib.CategoryTheory.Limits.Opposites import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.Products im...
EssentialFiniteness.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.FiniteType import Mathlib.RingTheory.Localization.Defs import Mathlib.RingTheory.TensorProduct.Basic /-! # Essentially of finite type algebras #...
classfun.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...
DegreeSum.lean
/- Copyright (c) 2020 Kyle Miller. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kyle Miller -/ import Mathlib.Algebra.BigOperators.Ring.Finset import Mathlib.Combinatorics.SimpleGraph.Dart import Mathlib.Combinatorics.SimpleGraph.Finite import Mathlib.Data.ZMod.Basic...
Kleene.lean
/- Copyright (c) 2022 Siddhartha Prasad, Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Siddhartha Prasad, Yaël Dillies -/ import Mathlib.Algebra.Order.Monoid.Canonical.Defs import Mathlib.Algebra.Ring.InjSurj import Mathlib.Algebra.Ring.Pi import Mathlib...
test_intro_rw.v
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Lemma test_dup1 : forall n : nat, odd n. Proof. move=> /[dup] m n; suff: odd n by []. Abort. Lemma test_dup2 : let n := 1 in False. Proof. move=> /[dup] m n; have : m = n :=...
DiscrTree.lean
/- Copyright (c) 2023 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Init import Lean.Meta.DiscrTree /-! # Additions to `Lean.Meta.DiscrTree` -/ namespace Lean.Meta.DiscrTree /-- Find keys which match the expression, or s...
LocallyCompactRegular.lean
/- Copyright (c) 2022 Damien Thomine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damien Thomine -/ import Mathlib.Topology.Sets.Compacts /-! # Second Baire theorem In this file we prove that a locally compact regular topological space has Baire property. -/ open...
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. (*************************...
action.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun ssrnotations eqtype. From mathcomp Require Import ssrnat div seq prime fintype bigop finset. From mathcomp...
Dual.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.Dual.Lemmas import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv import Mathlib.LinearAlgebra.QuadraticForm.Prod /-! # Quadratic form stru...
StacksAttribute.lean
import Mathlib.Tactic.StacksAttribute import Mathlib.Util.ParseCommand /-- info: No tags found. -/ #guard_msgs in #stacks_tags namespace X @[stacks A04Q "A comment", kerodon B15R "Also a comment"] theorem tagged : True := .intro end X /-- info: some ([Stacks Tag A04Q](https://stacks.math.columbia.edu/tag/A04Q) (A ...
Defs.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.Defs import Mathlib.Algebra.Notation.Pi.Def...
Defs.lean
/- Copyright (c) 2021 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, William Sørensen, Robin Arnez -/ import Mathlib.Logic.Equiv.Defs import Mathlib.Tactic.MkIffOfInductiveProp import Mathlib.Tactic.PPWithUniv /-! # Small types A type is `...
Basic.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.CategoryTheory.Functor.Currying import Mathlib.CategoryTheory.Limits.Preserves.Limits /-! # (Co)limits in functor categories. We show that if `D` has lim...
Star.lean
/- Copyright (c) 2018 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Mario Carneiro, Yury Kudryashov, Heather Macbeth -/ import Mathlib.Analysis.CStarAlgebra.Basic import Mathlib.Topology.ContinuousMap.Bounded.Normed import Mathlib...
NoZeroDivisors.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.RingTheory.PowerSeries.Order import Mathlib.RingTheory.Ideal.Maps /-! # Power series over rings with no zero divisors This file proves, us...
CircleIntegral.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.Analytic.IsolatedZeros import Mathlib.Analysis.SpecialFunctions.Complex.CircleMap import Mathlib.Analysis.SpecialFunctions.NonIntegrable /-...
EssentiallySmall.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.Limits.Shapes.Products import Mathlib.CategoryTheory.EssentiallySmall /-! # Limits over essentially small indexing categories If `C` has...
Preorder.lean
/- Copyright (c) 2025 Sina Hazratpour. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sina Hazratpour, Joël Riou -/ import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts /-! # (Co)limits in a preorder category We provide basic results about the nullary and bina...
RingQuot.lean
/- Copyright (c) 2020 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.Algebra.RingQuot import Mathlib.Algebra.Star.Basic /-! # The *-ring structure on suitable quotients of a *-ring. -/ namespace RingQuot universe u variabl...
Dual.lean
/- Copyright (c) 2020 Heather Macbeth. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Heather Macbeth -/ import Mathlib.Analysis.LocallyConvex.Polar import Mathlib.Analysis.NormedSpace.HahnBanach.Extension import Mathlib.Analysis.NormedSpace.RCLike import Mathlib.Data....
Shift.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 import Mathlib.Algebra.Ring.NegOnePow import Mathlib.CategoryTheory.Shift.Quotient import Mathlib.CategoryTheory.Linear.LinearF...
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...
PureCoherence.lean
/- Copyright (c) 2024 Yuma Mizuno. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yuma Mizuno -/ import Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence import Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes /-! # Coherence tactic for bicategories We provide ...
Quotient.lean
/- Copyright (c) 2024 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang, Riccardo Brasca -/ import Mathlib.LinearAlgebra.Dimension.DivisionRing import Mathlib.LinearAlgebra.FreeModule.PID import Mathlib.LinearAlgebra.FreeModule.StrongRankCond...
Subalgebra.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.Algebra.Subalgebra.Lattice import Mathlib.RingTheory.Finiteness.Basic import Mathlib.RingTheory.Finiteness.Bilinear /-! # Subalgebras that are...
mxred.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 div. From mathcomp Require Import choice fintype finfun bigop fingroup perm order. From ...
Countable.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Data.Finsupp.Encodable import Mathlib.Data.Set.Countable import Mathlib.LinearAlgebra.Finsupp.LinearCombination /-! # Countable modules -/ noncomputa...
ZPow.lean
/- Copyright (c) 2021 Yakov Pechersky. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yakov Pechersky -/ import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.LinearAlgebra.Matrix.Symmetric /-! # Integer powers of square matrices In this file, we defi...
Associator.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Robin Carlier -/ import Mathlib.CategoryTheory.Sums.Basic /-! # Associator for binary disjoint union of categories. The associator functor `((C ⊕ D) ⊕ E) ⥤ (C ⊕ (D ⊕ E))`...
Cast.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.Order.Group.Abs import Mathlib.Algebra.Order.Ring.Int import Mathlib.Data.Nat.Cast.Order.Ring /-! # Order properties of cast of integers This...
NaturalTransformation.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.CategoryTheory.Adjunction.FullyFaithful import Mathlib.CategoryTheory.Monoidal.Functor import Mathlib.CategoryTheory.ObjectProperty.FullSubcategory /-! # ...
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.
TruncLEHomology.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.Homology.Embedding.TruncGEHomology import Mathlib.Algebra.Homology.Embedding.TruncLE import Mathlib.Algebra.Homology.HomologySequence import Mathlib.Alge...
Prod.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Eric Wieser -/ import Mathlib.Algebra.Algebra.Prod import Mathlib.Algebra.Group.Graph import Mathlib.LinearAlgebra.Span....
Polynomial.lean
import Mathlib.Algebra.Polynomial.Basic import Mathlib.Algebra.Module.ULift open Polynomial def p0 : ℕ[X] := ⟨⟨{}, Pi.single 0 0, by intro; simp [Pi.single, Function.update_apply]⟩⟩ example : reprStr p0 = "0" := by native_decide example : reprStr (Option.some p0) = "some 0" := by native_decide example : (reprPrec p...
SwapVar.lean
/- Copyright (c) 2022 Arthur Paulino. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Arthur Paulino -/ import Lean.Elab.ElabRules import Mathlib.Util.Tactic /-! # Defines the `swap_var` tactic Swap the names of two hypotheses. -/ open Lean Meta Elab.Tactic namespac...
Free.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.Algebra.Module.FinitePresentation import Mathlib.RingTheory.Localization.Finiteness import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition import Mathli...
Inverse.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.Deriv.Comp import Mathlib.Analysis.Calculus.FDeriv.Equiv /-! # Inverse function theorem - the easy half In this file we prove tha...
binomial.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 div fintype tuple ...
Card.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Algebra.NoZeroSMulDivisors.Basic import Mathlib.SetTheory.Cardinal.Basic /-! # Cardinality of a module This file proves that the cardinality of...
imset2_finset.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Check @imset2_pair.
Abs.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.Group.Defs import Mathlib.Algebra.Order.Group.Unbundled.Abs import Mathlib.Algebra.Order...
Proper.lean
/- Copyright (c) 2024 Christian Merten, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten, Andrew Yang -/ import Mathlib.AlgebraicGeometry.Morphisms.Separated import Mathlib.AlgebraicGeometry.Morphisms.Finite /-! # Proper morphisms A morph...
TuringMachine.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.Computability.Tape import Mathlib.Data.Fintype.Option import Mathlib.Data.Fintype.Prod import Mathlib.Data.Fintype.Pi import Mathlib.Data.PFun import M...
qfpoly.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype tuple div bigop binomial finset finfun. From mathcomp Require Import ssralg countalg finalg poly polydiv qpoly perm. From mathcomp Require Import fingroup falgebra fiel...
Complemented.lean
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Normed.Operator.Banach import Mathlib.Topology.Algebra.Module.FiniteDimension /-! # Complemented subspaces of normed vector spaces A submo...
Composition.lean
/- Copyright (c) 2020 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Johan Commelin -/ import Mathlib.Analysis.Analytic.Basic import Mathlib.Combinatorics.Enumerative.Composition /-! # Composition of analytic functions In this fi...
HalfPlane.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.Complex.Basic import Mathlib.Topology.Instances.EReal.Lemmas /-! # Half-planes in ℂ are open We state that open left, right, upper and lower h...
DeprecatedSyntaxLinter.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa, Jeremy Tan, Adomas Baliuka -/ import Lean.Elab.Command -- Import this linter explicitly to ensure that -- this file has a valid copyright header and module docstring. im...
GramSchmidtOrtho.lean
/- Copyright (c) 2022 Jiale Miao. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jiale Miao, Kevin Buzzard, Alexander Bentkamp -/ import Mathlib.Analysis.InnerProductSpace.PiL2 import Mathlib.LinearAlgebra.Matrix.Block /-! # Gram-Schmidt Orthogonalization and Orthonor...
Monoidal.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou, Jack McKoen -/ import Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex import Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory import Mathlib.CategoryTheory.Monoidal.T...
Domain.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.Degree.Operations /-! # Univariate polynomials form a domain ## Main results * `Polynom...
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...
Symmetric.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn, Antoine Labelle, Rémi Bottinelli -/ import Mathlib.Combinatorics.Quiver.Path import Mathlib.Combinatorics.Quiver.Push /-! ## Symmetric quivers and arrow reversal This file co...
PerfectSpace.lean
/- Copyright (c) 2025 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Analysis.SpecificLimits.Normed import Mathlib.Topology.Perfect /-! # Vector spaces over nontrivially normed fields are perfect spaces -/ open F...
Extrema.lean
/- Copyright (c) 2020 Frédéric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Frédéric Dupuis -/ import Mathlib.Analysis.Convex.Function import Mathlib.Topology.Algebra.Affine import Mathlib.Topology.Order.LocalExtr import Mathlib.Topology.MetricSpace.Pseudo.Le...
format_table.lean
import Mathlib.Util.FormatTable /-- info: | first | second header | third \| header | | :-------------- | :-------------: | --------------: | | item number one | item two | item c | | the fourth item | the fourth item | escape \| this | | align left | align center | align right...
Trace.lean
/- Copyright (c) 2022 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ import Mathlib.RingTheory.Trace.Basic import Mathlib.FieldTheory.Finite.GaloisField /-! # The trace and norm maps for finite fields We state several lemmas about the ...
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...
BooleanAlgebra.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Bryan Gin-ge Chen -/ import Mathlib.Order.BooleanAlgebra.Defs import Mathlib.Order.BooleanAlgebra.Basic import Mathlib.Tactic.Linter.DeprecatedModule deprecated_modul...
Comp.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.EffectiveEpi.Basic /-! # Composition of effective epimorphisms This file provides `EffectiveEpi` instances for certain composition...
Kronecker.lean
/- Copyright (c) 2021 Filippo A. E. Nuccio. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Filippo A. E. Nuccio, Eric Wieser -/ import Mathlib.Data.Matrix.Basic import Mathlib.Data.Matrix.Block import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.Linear...
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.
Finite.lean
/- Copyright (c) 2021 Jordan Brown, Thomas Browning, Patrick Lutz. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jordan Brown, Thomas Browning, Patrick Lutz -/ import Mathlib.Algebra.Group.Subgroup.Finite import Mathlib.GroupTheory.Commutator.Basic import Mathlib.Grou...
Monoid.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, Mitchell Lee -/ import Mathlib.Algebra.BigOperators.Finprod import Mathlib.Algebra.BigOperators.Pi import Mathlib.Algebra.Group.Submonoid.Basic import M...
Basic.lean
import Mathlib.Tactic.CategoryTheory.Monoidal.Basic open CategoryTheory Mathlib.Tactic BicategoryLike open MonoidalCategory universe v u variable {C : Type u} [Category.{v} C] [MonoidalCategory C] variable {X Y Z W : C} (f : X ⟶ Y) (g : Y ⟶ Z) example (f : U ⟶ V ⊗ (W ⊗ X)) (g : (V ⊗ W) ⊗ X ⟶ Y) : f ⊗≫ g = f ≫ (...
FinCoercions.lean
-- We verify that after importing Mathlib, -- we have not introduced a global coercion from `Nat` to `Fin n`. -- Such coercions introduce unexpected invisible wrap-around arithmetic. -- `open Fin.CommRing ...` *does* introduce such a coercion. import Mathlib set_option pp.mvars false -- We first verify that there is...
Isometries.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.QuadraticForm.TensorProduct import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv /-! # Linear equivalences of tensor products as isometrie...
Spaces.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.Grothendieck import Mathlib.CategoryTheory.Sites.Pretopology import Mathlib.CategoryTheory.Limits.Lattice import Mathlib.Topology.Sets...
Finsupp.lean
/- Copyright (c) 2018 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Jens Wagemaker, Aaron Anderson -/ import Mathlib.Data.Finsupp.Multiset import Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors /-! # Factors as finsupp ...
FindSyntax.lean
/- Copyright (c) 2024 Damiano Testa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Damiano Testa -/ import Lean.Elab.Command import Mathlib.Init /-! # The `#find_syntax` command The `#find_syntax` command takes as input a string `str` and retrieves from the enviro...
PUnit.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Group.PUnit import Mathlib.Algebra.Order.AddGroupWithTop /-! # Instances on PUnit This file collects facts about ordered algebraic structures on the one...
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...
mxrepresentation.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...