chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
7,536 | lean_file_chunk | 2c9ecf7ff3342939027ea95ef513a91817ff91a60aab8b25bc4307ba79776ed0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
public import Mathlib.Topology.Algebra.Module.Spaces.WeakDual
/-!
# Topology of pointwise ... |
9,107 | lean_file_chunk | 7e1e2b8d53ff8955c2a319dff7778fc54a4c938c5ed9055995799563596e6648 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Frรฉdรฉric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Topology.Algebra.Module.Spaces.WeakDual
public import Mathlib.Algebra.Algebra.Spectrum.Basic
public import Mathlib.Topology.Continuous... |
16,121 | lean_file_chunk | 629354f5ec12bd096ee274946fb350a332639327d525b49f570fa72654b5b826 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Topology.Algebra.Module.Multilinear.Topology
public import Mathlib.Topology.Algebra.Module.Alternating.Basic
/-!
# Topology on contin... |
23,906 | lean_file_chunk | 7e28a9da00685133bceb0120bad23ccaef44274908087b6e92495a6327782450 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth, Sรฉbastien Gouรซzel
-/
module
public import Mathlib.LinearAlgebra.Alternating.Basic
public import Mathlib.LinearAlgebra.BilinearMap
public import Math... |
2,332 | lean_file_chunk | 5e75a65ff0662ad7557add5e66f577372c80a6e9b2dff9fd6d81969ef03eaae7 | lean_source_file | pkg_mathlib_source_file_chunks | [TopologicalSpace M] [AddCommMonoid M'] [Module R M'] [TopologicalSpace M'] [AddCommMonoid N]
[Module R N] [TopologicalSpace N] [ContinuousAdd N] [ContinuousConstSMul R N] [AddCommMonoid N']
[Module R N'] [TopologicalSpace N'] [ContinuousAdd N'] [ContinuousConstSMul R N']
/-- `ContinuousAlternatingMap.compContinuo... |
8,918 | lean_file_chunk | 3fd750c67bf7d1700405a15774d92659745a6fd522a66572a5bffa99463b335d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Topology.Sheaves.SheafCondition.Sites
/-!
# Another version of the sheaf condition.
Given a family of open sets `U : ฮน โ Opens X` we can f... |
16,757 | lean_file_chunk | e027b429afcd005bebbee96ab7608072d9f943de803442e6e1029e96bbf28ca2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Category.Pairwise
public import Mathlib.CategoryTheory.Limits.Constructions.BinaryProducts
public import Mathlib.CategoryTheo... |
9,894 | lean_file_chunk | d25f9167b89f68d8c8be47b3573426cf089435be506f7524ca84777737ee68e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.CategoryTheory.Sites.Spaces
public import Mathlib.Topology.Sheaves.Sheaf
public import Mathlib.CategoryTheory.Sites.DenseSubsite.Basic... |
10,967 | lean_file_chunk | 8bde3fb788798289a1db0e51ba3b765627b77855a2bf0467900db6e4ee436afe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Justus Springer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Justus Springer
-/
module
public import Mathlib.Topology.Sheaves.Forget
public import Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections
/-!
# The sheaf condition in term... |
16,182 | lean_file_chunk | 18de35c1ee95d038d6b6009ae0174294fe12e7b0c9a530cced498198371cf67f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
public import Mathlib.CategoryTheory.Limits.Shapes.Products
public import Mathlib.Topology.Sheaves.S... |
1,889 | lean_file_chunk | 7e8cc617af4f083c684a3b9148d30116ad9ecc866c7412c8aa214e91419315f2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Init
public import Lean.PrettyPrinter.Delaborator.Basic
/-!
# Additions to the delaborator
-/
@[expose] public section
namespace Lean.Prett... |
3,952 | lean_file_chunk | c4b4b17883c33a23aeadb40e63330c63d5bade77f69139edd189ff2dbfc218ad | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Init
public import Lean.HeadIndex
public import Lean.Meta.ExprLens
public import Lean.Meta.Check
/-!
# Find the positions of a pat... |
5,077 | lean_file_chunk | f568b7f1523d24ee70cf4bdb308bb5ebdaa17e28c964097a43cc259ce1d9661e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
public import Lean.Meta.AppBuilder
public import Lean.Meta.Coe
/-!
# Additions to `Lean.Meta.Basic`
Likely these already exist somewh... |
6,213 | lean_file_chunk | 420df18866cd0be1c151489390c3f064aa94a8d3ca871e330b6ff04d853e43c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Gabriel Ebner, Floris van Doorn
-/
module
public import Mathlib.Init
public import Lean.Elab.Tactic.Simp
public import Lean.Meta.DiscrTree
/-!
# Helper functions for usin... |
18,367 | lean_file_chunk | 67fdb3fb4e519fdd92cbc1facff1108cdfbaab59b605591ca8e375be6526403f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Lean.Meta.Tactic.Cleanup
public meta import Lean.Meta.Tactic.Refl
public import Mathlib.Logic.IsEmpty.Defs
/-!
# Additions to `Lean.Meta.CongrTheorem... |
7,740 | lean_file_chunk | 411eef9b489ca64edec3e6f4b31ff32ca9c19fe434c090a91eb6334384217431 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Lean.Meta.RefinedDiscrTree.Lookup
public import Mathlib.Lean.Meta.RefinedDiscrTree.Initialize
/-!
A discrimination tree for the pur... |
1,702 | lean_file_chunk | 0e8a15f20ff6b45e91f12f956a8f5b7152de01116d2df40ac37f416ed767ee06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
/-!
# Additions to `Lean.Meta.DiscrTree`
-/
@[expose] public section
namespace Lean.Meta.DiscrTree
/--
Find keys which match the ex... |
1,884 | lean_file_chunk | b7f2c8bedca21113fb325baec5ce912ac78ae2026346518bb144fd6662c1b33c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Kim Morrison
-/
module
public import Mathlib.Init
public import Lean.ToExpr
/-!
# Additional operations on Expr and rational numbers
This file defines some operatio... |
849 | lean_file_chunk | b26b82c4b8547d3bd6329db347afc481f5ff6d260e1ac74bbc831973e1c98248 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller
-/
module
public import Mathlib.Data.Set.CoeSort
/-!
# Additional Expr recognizers needing theory imports
-/
@[expose] public section
namespace Lean.Expr
/-- If `e` is a... |
1,547 | lean_file_chunk | a50f9e5ff1494d2f3b7550d3fbfdb30f19552600c3609ff436cd5852821f189b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Kim Morrison, Keeley Hoek, Robert Y. Lewis,
Floris van Doorn, Edward Ayers
-/
module -- shake: keep-all
public import Lean.Expr
public import Mathlib.Uti... |
22,513 | lean_file_chunk | e560e1cc7a2ef3b19354e0a3b0034c2a6febe9d5f7ed0442feff28c57ef824b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Kim Morrison, Keeley Hoek, Robert Y. Lewis,
Floris van Doorn, Edward Ayers, Arthur Paulino, Thomas R. Murrills
-/
module
-- Import this linter explicitly... |
4,925 | lean_file_chunk | 829747703d0c42c6dccc35c0489b764803634a17c04b0a29b9367745b5acd1f8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Thomas R. Murrills
-/
module
public import Mathlib.Lean.Environment
public import Lean.Server.InfoUtils
public import Lean.Meta.TryThis
public import Batteries.Tactic.Li... |
891 | lean_file_chunk | 249a522852e819df008054c4b8a7a4e1a04f1a58fd10de187419d6fb6f906dd9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kyle Miller. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kyle Miller, Thomas R. Murrills
-/
module
public import Mathlib.Init
public import Lean.Elab.Term
/-!
# Additions to `Lean.Elab.Term`
-/
public meta section
namespace Lean.Elab.Term
... |
5,295 | lean_file_chunk | b77aee3cfce45c28405ec6b4673d454888bc118569befb145d994eaae45e4eda | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Kim Morrison
-/
module
import Mathlib.Init
public import Lean.Message
public import Lean.Meta.Basic
/-!
# Tools for extracting `Expr`s from `MessageData` nodes
This file ... |
3,200 | lean_file_chunk | d7697f1187723f2c9bbc90b4700112dc0cb9fa2948a3a4c02656f92f381edb5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
import Mathlib.Init
public import Lean.Message
public import Std.Data.HashSet.Basic
/-!
# Utilities for analyzing `MessageData`
Utility functions for working w... |
1,038 | lean_file_chunk | 109b61deee19002e08bb958f7988eee68a5cef2eb40f6fb3c62b0cf052095db9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Patrick Massot, Kyle Miller
-/
module
public import Mathlib.Init
public import Lean.Meta.Tactic.Rewrite
/-!
# Additional declarations for `Lean.Meta.Tactic.Rewrite`
-/
@... |
12,404 | lean_file_chunk | 32f3e5aaaea02223238eabcd373486b9295f7c8e3c51d997c289b2d2edb9d93c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Lean.Meta.RefinedDiscrTree.Encode
/-!
# Matching with a RefinedDiscrTree
This file defines the matching procedure for the `Refined... |
11,858 | lean_file_chunk | 5f6ad69effbaa33a9cfdd1b86af0cdb22c84cf434d2542407f8297eeeedc9fc3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Lean.Meta.RefinedDiscrTree.Basic
public import Lean.Meta.CompletionName
/-!
# Constructing a RefinedDiscrTree
`RefinedDiscrTree` i... |
12,610 | lean_file_chunk | 5db07ea6ef85f6d265b3919784c1f93c3eb0112768ce6fea3ee12a734c799ecc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Init
/-!
# Basic Definitions for `RefinedDiscrTree`
We define
* `Key`, the discrimination tree key
* `LazyEntry`, the partial, laz... |
12,696 | lean_file_chunk | 3e35acaa8c6cefc4904f38e1cd3de9dc1dae53303fdd04bde545baa856fee37f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Lean.Meta.RefinedDiscrTree.Basic
public import Lean.Meta.DiscrTree
public import Lean.Meta.LazyDiscrTree
import all Lean.Meta.DiscrT... |
941 | lean_file_chunk | ad6a1d05df2c3d0d8e0890488d26a130812e9fd35cd250ae03902948d5cd7645 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Lean.Elab.SyntheticMVars
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and module docstring.
public imp... |
664 | lean_file_chunk | 6857a773e513ab943261046771dea1866cf70c8b702b01dffbd464eb7663613a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jon Eugster
-/
module
public import Mathlib.Lean.Meta
/-!
# Additions to `Lean.Elab.Tactic.Basic`
-/
@[expose] public section
open Lean Elab Tactic
namespace Le... |
9,250 | lean_file_chunk | 239cd9788e73ba910f0d805be3355926b363770591d10fb924f01bad1ee61c4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
module
public import Mathlib.Dynamics.TopologicalEntropy.NetEntropy
/-!
# Topological entropy of subsets: monotonicity, closure, union
This file contains general r... |
11,820 | lean_file_chunk | e693e45f182d36c60ff8b334a778788f0d518875418134c50d710d6d8caff01e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone
-/
module
public import Mathlib.Dynamics.TopologicalEntropy.CoverEntropy
/-!
# Topological entropy of the image of a set under a semiconjugacy
Consid... |
23,990 | lean_file_chunk | 148a49d2633d5cb86ca2fe8f905bf6b3fb381a49fd083a7ddaf52ba5cad981fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone
-/
module
public import Mathlib.Analysis.Asymptotics.ExpGrowth
public import Mathlib.Data.ENat.Lattice
public import Mathlib.Data.Real.ENatENNReal
pub... |
1,969 | lean_file_chunk | f5928b7f7c3745f9bdac2fd02c4c4fb9c0dfc343bd6b288760062ffa58cda72e | lean_source_file | pkg_mathlib_source_file_chunks | exact (coverEntropyEntourage_antitone T F si_U).trans
(le_iSupโ (f := fun (i : ฮน) (_ : p i) โฆ coverEntropyEntourage T F (s i)) i h_i)
lemma coverEntropyInf_eq_iSup_basis {ฮน : Sort*} {p : ฮน โ Prop} {s : ฮน โ SetRel X X}
(h : (๐ค X).HasBasis p s) (T : X โ X) (F : Set X) :
coverEntropyInf T F = โจ (i : ฮน) (_ : ... |
19,448 | lean_file_chunk | cf2cfcd09f966f77ea73836e907e040bb75aad622ddfe378f0f28deb0e8aad4c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone
-/
module
public import Mathlib.Dynamics.TopologicalEntropy.CoverEntropy
/-!
# Topological entropy via nets
We implement Bowen-Dinaburg's definitions... |
6,391 | lean_file_chunk | 56d5aaa1b67cd1eddb7303a10a78c9ace6b20ff6b5b3b4b8a106d23c05e7d999 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone
-/
module
public import Mathlib.Data.Nat.Lattice
public import Mathlib.Topology.UniformSpace.Basic
/-!
# Dynamical entourages
Bowen-Dinaburg's defin... |
4,801 | lean_file_chunk | df5444c3be51db2b00601fb68c011c03f34ca8244b7d226b100a1af8eed5c79a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Lua Viana Reis, Oliver Butterley
-/
module
public import Mathlib.Dynamics.BirkhoffSum.Basic
public import Mathlib.Algebra.Module.Basic
/-!
# Birkhoff average
In th... |
3,879 | lean_file_chunk | c03b9971d741341c06fa52ef9d9ff066999ffc87fb567c37dbad54b8d94189de | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.FixedPoints.Basic
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
# Birkhoff sums
In this file we define ... |
1,807 | lean_file_chunk | abeabd790861e921b7ef3c561dff83edbbc59541bc04235c57eb7c65b5582e91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Butterley. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Butterley, Lua Viana Reis
-/
module
public import Mathlib.Dynamics.BirkhoffSum.Average
public import Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving
/-!
# Birkhoff sum ... |
6,097 | lean_file_chunk | 5a97bae485154a38038483d1eddc1570a45deb7d65ed73a7ac817fd56e0f5bf1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Dynamics.BirkhoffSum.Average
/-!
# Birkhoff average in a normed space
In this file we pr... |
1,861 | lean_file_chunk | 2e59f1513245fa39c488a5fb58e903225976f1739eae43ec1762766d0e857b3d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
public import Mathlib.Dynamics.FixedPoints.Basic
/-!
# Results about pointwise operations on sets wi... |
1,272 | lean_file_chunk | 404bede3b042f1ed7cf997ae72082660b3ddc3609f0eb2acffefa62b23437ff8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Johannes Hรถlzl
-/
module
public import Mathlib.Dynamics.FixedPoints.Basic
public import Mathlib.Topology.Separation.Hausdorff
/-!
# Topological properties of fixed ... |
6,458 | lean_file_chunk | 1386bb04b721f78d3b56a260b6df6003189892496f86c54cfe3ddfcecd4cf94c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.End
public import Mathlib.Data.Set.Function
/-!
# Fixed points of a self-map
In this file we define
* the predicate `... |
11,076 | lean_file_chunk | 5b7fea7dbf3bffbdcdfd94106880f2380a5b4472717ffb0da2c3e254ebe4e6dc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.MeasureTheory.Measure.AEMeasurable
public import Mathlib.Order.Filter.EventuallyConst
/-!
# Measure-preserving maps
We say that `f :... |
7,597 | lean_file_chunk | 4cfe31850342bface844c8ce7fb2a6005ec799f264747e221b952b8dea8948fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.Dynamics.FixedPoints.Prufer
public import Mathlib.Dynamics.Ergodic.Ergodic
public import Mathlib.... |
5,237 | lean_file_chunk | 0ce47a8cd8c84b34872571bcfddd3a346553686806be8ddeca36a883bc11b6a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Convex.Extreme
public import Mathlib.Dynamics.Ergodic.Function
public import Mathlib.Dynamics.Ergodic.RadonNikodym
public imp... |
5,044 | lean_file_chunk | 06c07ffa989d743c005f3eb76e8336bb00030eb33bd81a848d5f4f73048798be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.Ergodic.MeasurePreserving
public import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
public import Mathlib.Topolo... |
5,214 | lean_file_chunk | 5128cc45cdd350808ac8c15aa2be82c2f9143f9fbb53ce2e9fba66fb6e70025a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.Ergodic.Ergodic
public import Mathlib.MeasureTheory.Function.AEEqFun
/-!
# Functions invariant under a (quasi)ergodic map
I... |
989 | lean_file_chunk | cfc708e66f0e244ab5ec6ca6e01539dd3bea879b9c75c78d7f059382c671396f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.Ergodic.Action.OfMinimal
public import Mathlib.Topology.Instances.AddCircle.DenseSubgroup
public import Mathlib.MeasureTheory... |
9,883 | lean_file_chunk | f51784d38f4271817f975ed836811161d8e8d2f6ac82fe53b77c8cbd5bdcea9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Dynamics.Ergodic.MeasurePreserving
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
/-!
# Ergodic maps and measures
Let `... |
11,803 | lean_file_chunk | 394d544131aacd920e69881468043cdfe4eaf19f29c7ba3a6f7c0749ca330d97 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
public import Mathlib.Dynamics.Ergodic.MeasurePreserving
public import Mathlib.Combinator... |
6,502 | lean_file_chunk | 22ec2a0d2ca617c0c3060c8d195ef2b5a4c7cfa126c6d1ae0e6c75775fdc4e59 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.GCDMonoid.Finset
public import Mathlib.Algebra.GCDMonoid.Nat
public import Mathlib.Data.Fintype.Card
public import Mathlib.Dat... |
23,994 | lean_file_chunk | 3d8465268bf163d2a7b101745defc631e8322142304595fa3f00f7f442ad73ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Algebra.Group.Action.Defs
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Algebra.Order.Sub.Basic
public import Ma... |
2,027 | lean_file_chunk | 361da235dcacf0803197a2c7d5f5cad5ea8085a1775cae05d97920cd87c7fa74 | lean_source_file | pkg_mathlib_source_file_chunks | conv_rhs => rw [โ Nat.mod_add_div n (period m a), pow_add, mul_smul,
pow_smul_eq_iff_period_dvd.mpr (dvd_mul_right _ _)]
@[to_additive (attr := simp)]
theorem zpow_mod_period_smul (j : โค) {g : G} {a : ฮฑ} :
g ^ (j % (period g a : โค)) โข a = g ^ j โข a := by
conv_rhs => rw [โ Int.emod_add_mul_ediv j (period g a)... |
23,941 | lean_file_chunk | 2f108be0e2724dd80bd549153766fa9727eb2522d4737a399eca5db1ba027e61 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.SpecificLimits.Basic
public import Mathlib.Order.Iterate
public import Mathlib.Order.SemiconjSup
public import Mathlib.Topolo... |
13,806 | lean_file_chunk | 2e397ad89601f120da11f5c867624bd7f1ab26a052de16c8d284b44d8a0085e5 | lean_source_file | pkg_mathlib_source_file_chunks | theorem translationNumber_eq_of_semiconjBy {f gโ gโ : CircleDeg1Lift} (H : SemiconjBy f gโ gโ) :
ฯ gโ = ฯ gโ :=
translationNumber_eq_of_dist_bounded 2 fun n =>
le_of_lt <| dist_map_zero_lt_of_semiconjBy <| H.pow_right n
theorem translationNumber_eq_of_semiconj {f gโ gโ : CircleDeg1Lift}
(H : Function.Sem... |
1,861 | lean_file_chunk | b02c5d4da64042860cfff3bc53e7549f36ffbccab6ccaf3676c793c4191d3627 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.Ergodic.Action.Basic
public import Mathlib.MeasureTheory.Group.Prod
/-!
# Regular action of a group on itself is ergodic
In... |
3,585 | lean_file_chunk | 5754de7ba6df5888a5f8fba2cbb7f7eebae8024b45de996cba5a49b509bfa80c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.MeasureTheory.Group.AEStabilizer
public import Mathlib.Dynamics.Ergodic.Ergodic
/-!
# Ergodic group actions
A group action of `G` on... |
11,995 | lean_file_chunk | 909236d1d2529fd2d5d4105245a9a6a88d5d286408a3545b011edc0c9b1a18df | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Dynamics.Ergodic.Action.Regular
public import Mathlib.MeasureTheory.Measure.ContinuousPreimage
public import Mathlib.MeasureTheory.Mea... |
19,978 | lean_file_chunk | b92761426f9598f49f77b4a531d8537f5c1e9185b6a9af70983e64dac558a8ef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.InnerProductSpace.LinearMap
public import Mathlib.LinearAlgebra.FiniteDimensional.Lemmas
publ... |
12,806 | lean_file_chunk | 04513b80f4f4e973ece590365789f1c45b8deb5770dea0439c3cdbf72998b3eb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Hampus Nyberg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hampus Nyberg, Yaรซl Dillies
-/
module
public import Mathlib.Analysis.InnerProductSpace.Completion
public import Mathlib.Analysis.InnerProductSpace.Positive
/-!
# Reproducing Kernel Hi... |
1,264 | lean_file_chunk | 35776d13d02c223dd50a7ee1b5ee13ec3f3e5d7858c66ad43d371f979eebc384 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.Convex.Uniform
public import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Convexity proper... |
5,403 | lean_file_chunk | 4cf4429c574e74f27d5c0d911d0cbf9d693fb80b157529e65fde5073f1c427c9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
public import Mathlib.Dynamics.BirkhoffSum.NormedSpace
/-!
# Von Neumann Mean Ergodic... |
23,750 | lean_file_chunk | 854fdce8e6136e1f162e1b4b1e10b13b2a982252b58f3be7839e3737ef9765be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Analysis.InnerProductSpace.Adjoint
public import Mathlib.LinearAlgebra.TensorProduct.Finiteness
public import Mathlib.RingTheory.TensorProduct... |
2,033 | lean_file_chunk | 397208c7372a89d69d2435bd53d21ef3514b8cda7ea87b0929235f23a3666e2c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.LinearAlgebra.Basis.MulOpposite
/-!
# Inner product space on `Hแตแตแต`
This file defines ... |
16,388 | lean_file_chunk | 64647f70916efe04aa737a3d33dc39192e975048fe2f623dcd64dd0f6b21f9d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.InnerProductSpace.Adjoint
public import Mathlib.Analysis.InnerProductSpace.Calculus
public import Mathlib.An... |
1,859 | lean_file_chunk | a4b45b32e55b182941834c1f2f779df4016ae458076ebe31e54570650a9d8902 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Frรฉdรฉric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Mathlib.Analysis.LocallyConvex.WeakOperatorTopology
/-!
# The weak operator topology in... |
16,351 | lean_file_chunk | e96c7282e17db6b2086fb41e0f7f45720ec1e8f9b09cf0d278d6016eda7fd3bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Analysis.Normed.Module.Ball... |
23,980 | lean_file_chunk | cfee2248c54dec1eb0d6829407b53d4e50453f4876fc1222d79bb0bc664a79b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Mathlib.Analysis.InnerProductSpace.Orientation
public import Mathlib.LinearAlgebra.Alter... |
477 | lean_file_chunk | bac79301df95040fb06398732ff2af6b37ad7d029e9baf325b8f7b0500d56277 | lean_source_file | pkg_mathlib_source_file_chunks | LinearIsometryEquiv.symm_apply_apply]
/-- The Kahler form on an oriented real inner product space of dimension 2 can be evaluated in terms
of a complex-number representation of the space. -/
theorem kahler_map_complex (f : E โโแตข[โ] โ)
(hf : Orientation.map (Fin 2) f.toLinearEquiv o = Complex.orientation) (x y : E)... |
3,867 | lean_file_chunk | fab0f71a8bb4f6daaa57b12753d97f6997ac832ec935daf1f99c39466f682350 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.Normed.Module.Completion
public import Mathlib.Analysis.InnerProductSpace.Continuous
/-!
# C... |
3,560 | lean_file_chunk | a51b65b99a2969f71af65c7b420b5d5a885a3d8637cc48afb9bbcc00b3572b68 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Analysis.InnerProductSpace.Positive
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic
public import Mathlib.A... |
7,988 | lean_file_chunk | 1c778e2509071aebbf904cd2cc87b80d910686724843790c096416e29604f17e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Analysis.InnerProductSpace.TensorProduct
public import Mathlib.RingTheory.Coalgebra.Basic
/-!
# Finite-dimensional inner product space with a... |
17,761 | lean_file_chunk | 645659bc24c3919e446f60811f2c1f94aa6d27b7ff676e6410792457b8a38169 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Basic
public import Mathlib.Analysis.Calculus.ContDiff.Operations
public import Mathlib.Analysis.Calculus.Ite... |
8,506 | lean_file_chunk | c98adde882eb1380751f0c5b23e5a676ffe042e95a90fc565a16a394411d22c6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yoh Tanimoto. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yoh Tanimoto
-/
module
public import Mathlib.Analysis.CStarAlgebra.Module.Constructions
public import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
/-!
# Standard subspaces o... |
14,197 | lean_file_chunk | 85b8c41f20d9cc79cd7a25791bba377240e203648f804bc3f57ebe7c80055bfb | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.LinearAlgebra.Orientation
/-!
# Orientations of real inn... |
23,963 | lean_file_chunk | 2cbae53f73e5fa65c8bed2be2409fa07fb53df6d66a9c47cf6126826988fdfdf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.Analysis... |
18,157 | lean_file_chunk | ab7802b5fe713b50272d8a2e85d124279e69ea4f2204199a83b86f8f6e111e2a | lean_source_file | pkg_mathlib_source_file_chunks | exact div_le_one_of_leโ (abs_real_inner_le_norm x y) (by positivity)
/-- The inner product of a vector with a multiple of itself. -/
theorem real_inner_smul_self_left (x : F) (r : โ) : โชr โข x, xโซ_โ = r * (โxโ * โxโ) := by
rw [real_inner_smul_left, โ real_inner_self_eq_norm_mul_norm]
/-- The inner product of a vecto... |
11,573 | lean_file_chunk | f97e5893c0dae627073d272f56173105b52ad3f0f63408d5568679c9d419af6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Analysis.InnerProductSpace.Orthonormal
/-!
# Subspaces of inner product spaces
This file defines the... |
10,049 | lean_file_chunk | 129869dc8edd6862d40ccaedafb150ad2ba29ad22d44b128c3c7b86790df44c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Niels Voss, Arnav Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Niels Voss, Arnav Mehta
-/
module
public import Mathlib.Analysis.InnerProductSpace.Positive
public import Mathlib.LinearAlgebra.Eigenspace.Zero
/-!
# Singular values for fin... |
17,157 | lean_file_chunk | 26e4066518d3d3af8f88e647951138d7297051b7b3475b2417f8574588723b7e | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.LinearAlgebra.Matrix.Block
/-!
# Gram-Schmidt Orthogon... |
4,791 | lean_file_chunk | b1bfcf2ce6b858b5f9134c93301f97c705beb2068ca5f106ac8d42208c644a7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.InnerProductSpace.Calculus
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Topology.MetricSpace.P... |
6,664 | lean_file_chunk | 4bb37f343885ca9ec3956de9534401798f97d48501129af3766b714baa02ecf1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jon Bannon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Bannon, Jack Cheverton, Samyak Dhar Tuladhar
-/
module
public import Mathlib.Analysis.InnerProductSpace.Spectrum
public import Mathlib.LinearAlgebra.Eigenspace.Pi
public import Mathli... |
9,285 | lean_file_chunk | ee147168a5fe3bf4cf4723bef730ff0fd9500ad9b31aaa8226b3d41b89dad9b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Topology.Algebra.Algebra
public import Mathlib.Analysis.InnerProductSpace.Convex
public import Mathlib.Algebra.Module.LinearMap.Rat
pu... |
23,989 | lean_file_chunk | 15f7b6e76818a244583b49eed26352f3af925b2291a39e8a5c93677f07fdadd3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
module
public import Mathlib.Analysis.InnerProductSpace.Projection.Basic
public import Mathlib.Analysis.Normed.Lp.lpSpace
public import Mathlib.Analysis.InnerProdu... |
1,179 | lean_file_chunk | b0a2982cb1ae1818d29e2a2f578c313950c6dda4d350da94c83fc35bc44c2d55 | lean_source_file | pkg_mathlib_source_file_chunks | HilbertBasis.mk b.orthonormal <| by
simpa only [โ OrthonormalBasis.coe_toBasis, b.toBasis.span_eq, eq_top_iff] using
@subset_closure E _ _
end
@[simp]
theorem _root_.OrthonormalBasis.coe_toHilbertBasis [Fintype ฮน] (b : OrthonormalBasis ฮน ๐ E) :
(b.toHilbertBasis : ฮน โ E) = b :=
HilbertBasis.coe_mk _ ... |
23,990 | lean_file_chunk | 25202c3fe173b96582fc881db17579a1b5e4787cef0653ab6c933e83ef4ca5b2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sรฉbastien Gouรซzel, Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Algebra.QuadraticDiscriminant
public import Mathlib.Analysis.LocallyConvex.WithSeminorms
public import... |
2,921 | lean_file_chunk | 33b7e70a8f4188a213c57f8290748a25991afc69dba16af549779f2d30a166f3 | lean_source_file | pkg_mathlib_source_file_chunks | topology to make sure it is defeq to an already existing topology. -/
@[reducible] def toNormedSpaceOfTopology
[tF : TopologicalSpace F] [IsTopologicalAddGroup F] [ContinuousConstSMul ๐ F]
(h : ContinuousAt (fun (v : F) โฆ cd.inner v v) 0)
(h' : IsVonNBounded ๐ {v : F | re (cd.inner v v) < 1}) :
letI :... |
23,999 | lean_file_chunk | d5d37691c067b0c932c551a936783ed8fc7f984df600e14e6c94fe762334e67a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Sรฉbastien Gouรซzel, Heather Macbeth
-/
module
public import Mathlib.Analysis.InnerProductSpace.Projection.FiniteDimensional
public import Mathlib.Analysis.Normed.Lp.PiLp
pu... |
23,944 | lean_file_chunk | a496d899c8e7a445e37fc19409b7985be4f24ab7566ff3e8deecdf8caee949e2 | lean_source_file | pkg_mathlib_source_file_chunks | protected def map {G : Type*} [NormedAddCommGroup G] [InnerProductSpace ๐ G]
(b : OrthonormalBasis ฮน ๐ E) (L : E โโแตข[๐] G) : OrthonormalBasis ฮน ๐ G where
repr := L.symm.trans b.repr
@[simp]
protected theorem map_apply {G : Type*} [NormedAddCommGroup G] [InnerProductSpace ๐ G]
(b : OrthonormalBasis ฮน ๐ ... |
8,835 | lean_file_chunk | f34f73f5d34fb0209d0edd3c4e580bd358d98fb0787b96fc55d7590d29faae72 | lean_source_file | pkg_mathlib_source_file_chunks | invFun b := โจhV.sigmaOrthonormalBasisIndexEquiv hn hV' โจi, bโฉ,
by simp [subordinateOrthonormalBasisIndex_def]โฉ
left_inv := by grind [subordinateOrthonormalBasisIndex_def, Fin.cast_eq_self]
right_inv := by grind
theorem DirectSum.IsInternal.card_filter_subordinateOrthonormalBasisIndex_eq
(hV' : OrthogonalFa... |
23,961 | lean_file_chunk | 115d84ba0689d46ec269dc22e5107974ea3f002ce50cd6726ead50356cb155ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Analysis.InnerProductSpace.Spectrum
public import Mathlib.Analysis.Matrix.Hermitian
public import Mathlib.Analysis.Matrix.Order
publ... |
937 | lean_file_chunk | b1db06b197ce19dbb6d4fe59e9cff0d5a99b2fba95b277c64a3ca7c2ad928ce7 | lean_source_file | pkg_mathlib_source_file_chunks | โ Real.sqrt_mul (hT.toLinearMap.nonneg_eigenvalues rfl _),
Real.sqrt_mul_self (hT.toLinearMap.nonneg_eigenvalues rfl _), mul_comm _ (โช_, _โซ_๐),
โ smul_eq_mul, smul_assoc, โ hT.isSymmetric.apply_eigenvectorBasis, โ map_smul, โ map_sum,
โ OrthonormalBasis.repr_apply_apply, OrthonormalBasis.sum_repr, coe_coe]... |
4,104 | lean_file_chunk | 9ba3dfc1ce6c922edc2be35b8132c9eacd4b612ea42fa9c8f3f1c76a04bdacd8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Daniel Roca Gonzรกlez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Roca Gonzรกlez
-/
module
public import Mathlib.Analysis.InnerProductSpace.Dual
/-!
# The Lax-Milgram Theorem
We consider a Hilbert space `V` over `โ`
equipped with a bou... |
1,880 | lean_file_chunk | 68e8e26a4538dde2926542da61b516e0e3f49ed4ac93dacbcc25937af8ca2db9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ivรกn Renison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivรกn Renison
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Analysis.InnerProductSpace.Spectrum
public import Mathlib.LinearAlgebra.Eigenspace.Cha... |
1,702 | lean_file_chunk | 0dfb7d1334740dacd5fe771054b4b75f7b0ba67d561bffdfed31d18acead562f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
module
public import Mathlib.Analysis.Normed.Operator.Conformal
public import Mathlib.Analysis.InnerProductSpace.LinearMap
/-!
# Conformal maps between inner product sp... |
23,972 | lean_file_chunk | b61aeaf84477681c1cb54b53ac6823788239ecf25746ddddfdbaedacef403eaa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Frรฉdรฉric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frรฉdรฉric Dupuis, Heather Macbeth
-/
module
public import Mathlib.Algebra.Star.UnitaryStarAlgAut
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Mathlib.Analysis.I... |
21,424 | lean_file_chunk | 7d347ce24a68a29912234ed91e8dcc79ec0c76e4084604a2c4998bb7dc68de7c | lean_source_file | pkg_mathlib_source_file_chunks | haveI := FiniteDimensional.complete ๐ E
haveI := FiniteDimensional.complete ๐ F
simpa using A.toContinuousLinearMap.orthogonal_ker
/-- 7.6(a) from [axler2024].
See `ContinuousLinearMap.orthogonal_range` for the infinite-dimensional version. -/
lemma orthogonal_range (A : E โโ[๐] F) : A.rangeแฎ = A.adjoint.ker :=... |
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