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 |
|---|---|---|---|---|---|
17,562 | lean_file_chunk | 5784b5b1e50bf91e71e48b51aa8fa17b4a32849ea03f4e9bff73b96e472eb5b9 | lean_source_file | pkg_mathlib_source_file_chunks | @[to_additive existing, deprecated (since := "2026-01-24")]
alias mem_emetric_ball_one_iff := mem_eball_one_iff
end ENorm
section ESeminormedMonoid
variable {E : Type*} [TopologicalSpace E] [ESeminormedMonoid E]
@[to_additive enorm_add_le]
lemma enorm_mul_le' (a b : E) : ‖a * b‖ₑ ≤ ‖a‖ₑ + ‖b‖ₑ := ESeminormedMonoid.... |
23,920 | lean_file_chunk | 4be6b5f9c01b0754d1b99d74ef06ffe9fecc1e0e82beb024e15ec5081c5b5f68 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Riccardo Brasca
-/
module
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Analysis.Normed.Group.Hom
public import Mathlib.Analysis.Normed.Oper... |
294 | lean_file_chunk | b46a2f31f051c3dea4588382e81f6f81c0eda6518f99410bc70a03056bad50a5 | lean_source_file | pkg_mathlib_source_file_chunks | { Ideal.Quotient.semiNormedCommRing I, Submodule.Quotient.normedAddCommGroup I with }
variable (𝕜 : Type*) [NormedField 𝕜]
instance Ideal.Quotient.normedAlgebra [NormedAlgebra 𝕜 R] : NormedAlgebra 𝕜 (R ⧸ I) :=
{ Submodule.Quotient.normedSpace I 𝕜, Ideal.Quotient.algebra 𝕜 with }
end Ideal |
15,082 | lean_file_chunk | 58c10f9aee14854f5949a8c618743f6c9033f0b82a4698780c84035b137d0069 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.PUnit
public import Mathlib.Algebra.Group.ULift
public import Mathlib.Analysis.Normed.Group.... |
16,128 | lean_file_chunk | 1c69f5a121f6ba40a735bfcf7c73cab7f776afc351dc15a96654cae79829952b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Topology.Algebra.Ring.Real
public import Mathlib.Topolog... |
21,108 | lean_file_chunk | 12185d51d5e95b0e012b7c54095c4d07eba1a0ed9af3bd359ea3e579013e939c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Group.Seminorm
public import Mathlib.Topology.Order.Real
public import Mathlib.Algebra.Ord... |
3,261 | lean_file_chunk | b17d8ea0b3dc2501238931a31489c33cb7c93072bfd4c58f2c89ed9d70ad9d13 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Analysis.Normed.Group.Uniform
public import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Completeness of normed groups
This file incl... |
4,110 | lean_file_chunk | d647bc6a8eea12b7ce887ca78deb6afa87e2f2cce3ab1223a60cbb889c959b2c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Algebra.Group.Subgroup.Defs
public import Mathlib.Analysis.Normed.Group.Basic
/-!
# Subgroups of normed (... |
2,025 | lean_file_chunk | 02130ea5a2227dd96d0c9481ab73b9b82c36658b6cf22d51dde65e57e34f4b0b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Algebra.Module.Submodule.LinearMap
public import Mathlib.Analysis.Normed.Group.Basic
/-! # Submodules of ... |
8,322 | lean_file_chunk | 5f949347b9c2ca8de1aa95187326d4007fedc0a9ccd8bd8cc7e232e81d7534ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Group.Continuity
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.... |
12,729 | lean_file_chunk | 79b8cc99995b6468315841badf55d2746a747f01d3e4c4c514883d0db7e7fb9c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Riccardo Brasca
-/
module
public import Mathlib.Analysis.Normed.Group.Constructions
public import Mathlib.Analysis.Normed.Group.Hom
public import Mathlib.CategoryTheor... |
6,372 | lean_file_chunk | ae2ac7d12c063e8c28f45b968a13d82b6ea95c54045cad8b953cc9958bcb472d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Normed.Group.InfiniteSum
public import Mathlib.Topology.Instances.ENNReal.Lemmas
/-!
# Continuity of series of functions... |
1,866 | lean_file_chunk | cf59342b63feaa8a1364fd91882bc05ab5af79467995f14982142291c2d5d532 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Analysis.Normed.Group.Uniform
/-!
# Negation on spheres and balls
In this file we define `InvolutiveNeg` and `Conti... |
23,967 | lean_file_chunk | d9f184e7b06b68dab1fe00aff3c87f1150656464514b8e049f1366026be71170 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 María Inés de Frutos-Fernández, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Yaël Dillies
-/
module
public import Mathlib.Data.NNReal.Defs
public import Mathlib.Order.ConditionallyCompleteLattice.Gr... |
6,264 | lean_file_chunk | d76c5f4f6a2c59bbce9bb82a14ad43b5243eab7e476a20fcda4f87e7066a0c87 | lean_source_file | pkg_mathlib_source_file_chunks | mul_max_of_nonneg _ _ NNReal.zero_le_coe]
gcongr
apply map_add_le_max
neg' := fun x => by simp_rw [map_neg_eq_map p] }⟩
instance [SMul R' ℝ] [SMul R' ℝ≥0] [IsScalarTower R' ℝ≥0 ℝ] [SMul R R'] [IsScalarTower R R' ℝ] :
IsScalarTower R R' (NonarchAddGroupSeminorm E) :=
⟨fun r a p => ext fun x ... |
6,019 | lean_file_chunk | b6098c9743bf88268c9cba72f84872e70072374c58cbeed7864c2e6baacca81c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
module
public import Mathlib.Analysis.Normed.Group.Hom
public import Mathlib.Analysis.SpecificLimits.Normed
/-! # Extending a backward bound on a normed group homom... |
1,641 | lean_file_chunk | 68ed56b9e8e42198046260180ce32c168343dbebc6aab27388b7f94de68c135d | 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.ContinuousMap.ZeroAtInfty
/-!
# ZeroAtInftyContinuousMapClass in normed additive groups
In this file we give a characterization of ... |
23,956 | lean_file_chunk | f1698857dbaf8ee339509125172946c3a0cba3dbf2684c7c22a49d93d3e47ab5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Analysis.Normed.Group.Int
public import Mathlib.Analysis.Normed.Group.Subgroup
public import Mathlib.Analysis.Normed.Group.Uniform
/-!
... |
5,938 | lean_file_chunk | 03a4819e41e8313ae553dd5cf69b453a10a1ceaccddc1f47522a99978c22e9f0 | lean_source_file | pkg_mathlib_source_file_chunks | theorem comp_range : (g.comp f).range = AddSubgroup.map g.toAddMonoidHom f.range := by
unfold range
rw [AddMonoidHom.map_range]
rfl
theorem incl_range (s : AddSubgroup V₁) : (incl s).range = s := by
ext x
exact ⟨fun ⟨y, hy⟩ => by rw [← hy]; simp, fun hx => ⟨⟨x, hx⟩, by simp⟩⟩
@[simp]
theorem range_comp_incl... |
3,956 | lean_file_chunk | 88741258372570b82c7b55fb728bba0f63ecbc98e0dfd557bbf7d0cb1ec58fa9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Group.Basic
/-!
# Norms on `ℝ` and `ℝ≥0`
We equip `ℝ`, `ℝ≥0`, and `ℝ≥0∞` with their natu... |
17,185 | lean_file_chunk | 31eab32249502a3efe225aebe39d965be1113a2b841c776a366aab9e754b0189 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Yury Kudryashov, Michał Świętek
-/
module
public import Mathlib.Analysis.Normed.Module.Dual
public import Mathlib.Analysis.Normed.Operator.Completeness
public import Mathl... |
7,980 | lean_file_chunk | a947ee213211f43ecbcbb72f4873fe03f7f87bb2dcb02b91b43f923acc52b83b | 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, Heather Macbeth
-/
module
public import Mathlib.Analysis.Convex.Cone.Extension
public import Mathlib.Analysis.Normed.Module.RCLike.Extend
public import Mathlib.Analy... |
9,169 | lean_file_chunk | f64d8a1d41148755f1defe3c4be4e386b91873f606bf06297334df766585e063 | 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: Alexander Bentkamp, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Convex.Jensen
public import Mathlib.Analysis.Convex.PathConnected
public import Mathlib.Analysis.Convex.T... |
4,435 | lean_file_chunk | 3a79f9bbfa1e4ca4e270aaba10e4e1efbab6587412818911c16b1aa4aeef44ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
module
public import Mathlib.LinearAlgebra.Ray
public import Mathlib.Analysis.Normed.Module.RCLike.Real
/-!
# Rays in a real normed vector space
In... |
6,429 | lean_file_chunk | e8de389221e3d78f879414426d147fab142518b27cc107759e6a94e1685005cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Module.RCLike.Real
public import Mathlib.Analysis.Normed.Module.RCLike.Basic
public import Mathlib.Analysis.Seminorm
... |
23,389 | lean_file_chunk | 22b94689413142515ccf1b155247222abf70f6b438c3348744ceb34097ebdda9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michał Świętek. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michał Świętek
-/
module
public import Mathlib.Analysis.Normed.Group.InfiniteSum
public import Mathlib.Analysis.Normed.Operator.BanachSteinhaus
public import Mathlib.LinearAlgebra.Fin... |
1,781 | lean_file_chunk | a029861ca25ce25b82538a7f17c7190737c48223de61668e99eebcdfaf092cc9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.Algebra.Module.TransferInsta... |
15,106 | lean_file_chunk | 9a4b881988a4dba75e0589820f1ccf8e741d6c8f1d763092cfa1f512969f0097 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Analysis.Normed.Operator.Banach
public import Mathlib.Topology.Algebra.Module.FiniteDimension
/-! # Continuous linear maps with a c... |
119 | lean_file_chunk | b747b77adfad3ce19b25ac7baab680f7d99ce3a044c635b85ecb29c5ee88b5a6 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.Normed.Group.Basic
deprecated_module (since := "2025-12-18") |
3,140 | lean_file_chunk | 285d31620d130ac693f4ce309520b6c1802ffe3639919dbad7f05bd27091515a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Normed.Group.Completion
public import Mathlib.Analysis.Normed.Operator.NormedSpace
public import Mathlib.Topology.Algebra.Uni... |
5,635 | lean_file_chunk | 6e45b697dc631bc3dcdf844e77cca845cebe7534f65882f063bab1afccbb479c | 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.Normed.Operator.Banach
public import Mathlib.Topology.Algebra.Module.FiniteDimension
/-!
# Complemented subspaces of normed ... |
23,954 | lean_file_chunk | 64c8dc73bf6582177d4a454dafe7bb34cf3ed9c8f2eddd44846de00763c5613f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Algebra.Pi
public import Mathlib.Algebra.Algebra.Prod
public import Mathlib.Algebra.Algebra.Rat
public import Ma... |
11,637 | lean_file_chunk | aac763d3f5507abd4580e705d185b3ec6c0ffd69b88ff430443d8f22e03e3418 | lean_source_file | pkg_mathlib_source_file_chunks | have : -y + x = (-1 : 𝕜) • (-x + y) := by simp; abel
rw [this, core.norm_smul]
simp
dist_triangle x y z := by
show ‖-x + z‖ ≤ ‖-x + y‖ + ‖-y + z‖
have : -x + z = (-x + y) + (-y + z) := by abel
rw [this]
exact core.norm_triangle _ _
edist_dist x y := by exact (ENNReal.ofReal_eq_coe_nnreal _)... |
23,997 | lean_file_chunk | 2a50123cab60c02f678de1316b0d86405678e0eba5ccbd9d36ace110766efb3f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
public import Mathlib.Analysis.Normed.Group.Lemmas
public import Mathlib.Analysis.Normed... |
12,966 | lean_file_chunk | ad131e8ff79a380b717c8643b7130810022e5a480bd609ba7e57c95c054ba682 | lean_source_file | pkg_mathlib_source_file_chunks | { LinearMap.toContinuousLinearMap.symm.trans (LinearEquiv.piRing 𝕜 E ι 𝕜) with
continuous_toFun := by
refine continuous_pi fun i => ?_
exact (ContinuousLinearMap.apply 𝕜 E (Pi.single i 1)).continuous
continuous_invFun := by
simp_rw [LinearEquiv.invFun_eq_symm, LinearEquiv.trans_symm, Linear... |
822 | lean_file_chunk | b1fb2a94e696f34dd153b16a1e32e2d8a90887dd51b6409d59cb2c21a10a4c0d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Rothgang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Rothgang
-/
module
public import Mathlib.Analysis.Normed.Module.TransferInstance
/-!
# Transfer normed algebraic structures from `α` to `Shrink α`
-/
@[expose] public sect... |
3,617 | lean_file_chunk | 7c3f09a1368161865adfbc7a7050cf25e68e3e9ab0cc0984e96a7b62df887e19 | 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.Analysis.Normed.Operator.LinearIsometry
public import Mathlib.Analysis.Normed.Operator.ContinuousLinearMap
public import Mathlib.Analysis.Norm... |
5,947 | lean_file_chunk | 872432d7f2a6af107310718355b5a5358ca7951d49ec4ed00cb33a9c15991ad7 | 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, Michał Świętek
-/
module
public import Mathlib.Analysis.LocallyConvex.WeakSpace
public import Mathlib.Analysis.Normed.Module.WeakDual
/-!
# The double dual of a nor... |
2,313 | lean_file_chunk | ad16122af321fa5ec565cb5f77965073f589ace074dbb4a874c3a190fde110fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Ilmārs Cīrulis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilmārs Cīrulis, Alex Meiburg
-/
module
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Data.Sign.Defs
/-!
# Normalized vector
Function that returns unit length vec... |
13,144 | lean_file_chunk | 8b5fe2f157254b2f0013e3a2667a67342292235836de17fae4c5be24654d53d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Algebra.Ring.Idempotent
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Order.Basic
public import Mathli... |
11,653 | lean_file_chunk | 98282da9804a88370bbfb490a4621122ea93178625149c197ea5b96d3fe19f4a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Convex.Contractible
public import Mathlib.Analysis.Convex.Topology
public import Mathlib.Analysis.Normed.Module.Convex
pu... |
7,659 | lean_file_chunk | cb1c9644e4fc245f642db927474437b96c6abd18c0f9539b059b68aaff876908 | 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, Michał Świętek
-/
module
public import Mathlib.Analysis.LocallyConvex.Polar
public import Mathlib.Analysis.Normed.Module.HahnBanach
public import Mathlib.Analysis.No... |
7,874 | lean_file_chunk | 3ef8b0484bbb6c67996c420545088c85d760842d88540232876627e8b0ce84a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Normed.Group.FunctionSeries
public import Mathlib.Analysis.SpecialFunctions.Log.Summable
public import Mathlib.Topology.Algebra... |
3,885 | lean_file_chunk | 4b54e9867129d2b8662fb7c7506ea7323501b953eb3e9ef05aa60f574361dccd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Normed.Module.Ray
public import Mathlib.Topology.Order.LocalExtr
/-!
# (Local) maximums in a normed space
In this file we p... |
3,159 | lean_file_chunk | c8d870111572b1e5f1f689fb6ce9cd61a441cac6f1200c32fa30b20d74d816ea | 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
-/
module
public import Mathlib.Analysis.Normed.Lp.PiLp
public import Mathlib.LinearAlgebra.Determinant
/-!
# Matrices are isomorphic with linear maps between Lp spaces
Th... |
23,929 | lean_file_chunk | baf248a9b719f350a834cb94099d4ccb7e95028cae7b292b15757b005840c50b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Jireh Loreaux
-/
module
public import Mathlib.Analysis.MeanInequalities
public import Mathlib.Data.Fintype.Order
public import Mathlib.LinearAlgebra.Matrix.Basis... |
23,971 | lean_file_chunk | a37d73f8d60ab8a6aa81b574e9c4fff49216dcf0df1e50586d5ea4b46b979c21 | lean_source_file | pkg_mathlib_source_file_chunks | def uniformEquiv [∀ i, UniformSpace (β i)] : PiLp p β ≃ᵤ (Π i, β i) where
toEquiv := WithLp.equiv p (Π i, β i)
uniformContinuous_toFun := uniformContinuous_ofLp p β
uniformContinuous_invFun := uniformContinuous_toLp p β
@[simp]
lemma toHomeomorph_uniformEquiv [∀ i, UniformSpace (β i)] :
(uniformEquiv p β).to... |
5,373 | lean_file_chunk | 116a6a3d80b1f60ddd60e728d26908c45ca0ac5eb2f2d698eb485826125f7cc4 | lean_source_file | pkg_mathlib_source_file_chunks | Basis.ofEquivFun (WithLp.linearEquiv p 𝕜 (ι → 𝕜))
@[simp]
theorem basisFun_apply [DecidableEq ι] (i) :
basisFun p 𝕜 ι i = single p i 1 := by
simp_rw [basisFun, Basis.coe_ofEquivFun, WithLp.coe_symm_linearEquiv, toLp_single]
@[simp]
theorem basisFun_repr (x : PiLp p fun _ : ι => 𝕜) (i : ι) : (basisFun p 𝕜 ι... |
2,266 | lean_file_chunk | 6220bd61195a4d3e05f4d23a0bd09971693bca2c7a5b25e6a9f7afc3c4ae0980 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Analysis.Normed.Lp.PiLp
public import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
/-!
# Measurable space structure on `WithLp`... |
6,574 | lean_file_chunk | c772b98fac20a7bf53cc4d0f83991ce98fbfab473e38ed0c21bc9e19052a8f7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Normed.Lp.PiLp
public import Mathlib.Analysis.Normed.Lp.lpSpace
public import Mathlib.Topology.ContinuousMap.Bounded.Normed
/-!
... |
23,971 | lean_file_chunk | 55a3a56839c58064e49414768435b8bea58503b4fc6f45f91b18fc1c26ecdcea | 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
-/
module
public import Mathlib.Analysis.MeanInequalities
public import Mathlib.Analysis.MeanInequalitiesPow
public import Mathlib.Analysis.SpecialFunctions.Pow.Conti... |
23,991 | lean_file_chunk | 6f7c538b5e2ad19ecf9f303983c9c921131176eba725fbba62c20a8bca367d3a | lean_source_file | pkg_mathlib_source_file_chunks | theorem norm_le_of_tsum_le (hp : 0 < p.toReal) {C : ℝ} (hC : 0 ≤ C) {f : lp E p}
(hf : ∑' i, ‖f i‖ ^ p.toReal ≤ C ^ p.toReal) : ‖f‖ ≤ C := by
rw [← Real.rpow_le_rpow_iff (norm_nonneg' _) hC hp, norm_rpow_eq_tsum hp]
exact hf
theorem norm_le_of_forall_sum_le (hp : 0 < p.toReal) {C : ℝ} (hC : 0 ≤ C) {f : lp E p}... |
5,592 | lean_file_chunk | a4487a9233085a8c04f1ade09e215dfb5e246f412024e9f00ffedef6c1899dbb | lean_source_file | pkg_mathlib_source_file_chunks | variable {ι : Type*} {l : Filter ι} [Filter.NeBot l]
theorem norm_apply_le_of_tendsto {C : ℝ} {F : ι → lp E ∞} (hCF : ∀ᶠ k in l, ‖F k‖ ≤ C)
{f : ∀ a, E a} (hf : Tendsto (id fun i => F i : ι → ∀ a, E a) l (𝓝 f)) (a : α) : ‖f a‖ ≤ C := by
have : Tendsto (fun k => ‖F k a‖) l (𝓝 ‖f a‖) :=
(Tendsto.comp (contin... |
23,945 | lean_file_chunk | ab8654e182ae2927cb106594295fb909e2bb37aea33f6d7f501cb5f0f23ca4ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Sébastien Gouëzel, Jireh Loreaux
-/
module
public import Mathlib.Analysis.MeanInequalities
public import Mathlib.Analysis.Normed.Lp.WithLp
/-!
# `L^p` distance on products ... |
23,996 | lean_file_chunk | 75cef7d54a11252ec9caab7a009241539ce12d303ea29eb7401ab6aefad22904 | lean_source_file | pkg_mathlib_source_file_chunks | theorem edist_fst_le [PseudoEMetricSpace α] [PseudoEMetricSpace β] (x y : WithLp p (α × β)) :
edist x.fst y.fst ≤ edist x y :=
(edist_proj_le_edist_aux p x y).1
theorem edist_snd_le [PseudoEMetricSpace α] [PseudoEMetricSpace β] (x y : WithLp p (α × β)) :
edist x.snd y.snd ≤ edist x y :=
(edist_proj_le_edis... |
449 | lean_file_chunk | 091a99c693f28bee564036a78f02d90cd450bce5e5486b522d224123bdeb74c2 | lean_source_file | pkg_mathlib_source_file_chunks | theorem coe_withLpProdUnique [Unique β] : ⇑(withLpProdUnique p 𝕜 α β) = WithLp.fst :=
rfl
/-- Left identity of the `L^p` product as a linear isometric equivalence. -/
@[simps! apply symm_apply]
def withLpUniqueProd [Unique α] : WithLp p (α × β) ≃ₗᵢ[𝕜] β :=
(withLpProdComm p 𝕜 α β).trans (withLpProdUnique p 𝕜 β... |
10,797 | lean_file_chunk | 1208fbe193276d064574b74d539709a99cf41d96af8e901a7c11774a5f76ef4e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.Module.TransferInstance
public import Mathlib.Data.ENNReal.Basic
public import Mathlib.RingTheory.Finiteness.Basic
/-! # The `WithLp`... |
4,804 | lean_file_chunk | 24cd05ccfacd1190981802f29f2a7f530c9c95baccdffefc1801b9020d72f9f1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Defs
public import Mathlib.LinearAlgebra.FiniteDimensional.Defs
public import Mathlib.MeasureTheory.Function.LpSpac... |
1,910 | lean_file_chunk | 547559d6b210131d9c0eae7d98555dfec2776a2d75eca91e3e279ca46e340bd4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Analysis.Normed.Field.Lemmas
public import Mathlib.Analysis.SpecificLimits.Basic
public import Mathlib.Topology.MetricSpace.ProperSpac... |
1,390 | lean_file_chunk | b3c485862f8aa8f60c4bb7ef3ead659ef476c5082909d3eb559313e646f852fe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Patrick Massot, Anatole Dedecker
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.Analysis.Normed.Ring.Lemmas
public import Mathlib.Orde... |
6,545 | lean_file_chunk | e570192c6fbb9b42d453c4260f62eea900c7eba1746df4ac1b7d10ad60965a55 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.Analysis.Normed.Algebra.Ultra
public import Mathlib.Analysis.Normed.Unbundled.SpectralNorm
public import Mathlib.FieldTheory.Minpoly.IsCon... |
5,924 | lean_file_chunk | 20ba8275b6bedd8eac806e0e25df06e535ecd167ca0bc9a7725ede76b4a5dcde | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.Analysis.Normed.Field.Approximation
public import Mathlib.Analysis.Normed.Field.Krasner
/-!
# Transfer algebraic properties from dense su... |
12,787 | lean_file_chunk | 9f9431610f8e306b12702186756cde2d93f27e7a0d21439384857ac4f9738973 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.Analysis.Normed.Group.Rat
public import Mathlib.Analysis.Normed.Ring.L... |
900 | lean_file_chunk | 8c833b54af9bbb4fa0e48bd58b3d99c9d9f0c3f0b3c115291f1bc403966086e3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.Algebra.Field.TransferInstance
public import Mathlib.Analysis.Normed.Field.Ba... |
6,698 | lean_file_chunk | e0092d7b1439fb183867efd12816afd41c88a53278ec8491415ce29019048bee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.Analysis.Normed.Ring.Ultra
public import Mathlib.Data.Nat.Choose.Sum
/-!
## Conditi... |
7,438 | lean_file_chunk | 952f28a8e7e2646df56f957e16f2b66a986f740ca18c5c06cf5cc1aa76f49126 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.Algebra.Polynomial.Splits
public import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
public import Mathlib.RingTheory.LocalRing.Basic
/... |
12,874 | lean_file_chunk | abda06c92831979f43f0cc7786abf920cc794ec2c24e1d3528910a297926e371 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Field.Subfield.Defs
public import Mathlib.Algebra.Order.Group.Pointwise.Interval
public import Mathlib.Analysis.... |
8,398 | lean_file_chunk | f66cd999907a127d5178c8293a15a4e926e8c4c7ed8f092cfc37f2c2f1aa3230 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Analysis.Normed.Field.Lemmas
public import Mathlib.Analysis.Normed.Field.TransferInstance
public import Mathlib.Analysis.Normed.Ri... |
10,844 | lean_file_chunk | 4201ddbae1d66d9e03750932a522cb6d563bf7f978eb655056285219e998475e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Analysis.Normed.Field.Lemmas
public import Mathlib.Analysis.Normed.Group.BallSphere
/-!
# Algebraic structures on un... |
5,183 | lean_file_chunk | 38d43fa04eb6d158a4f07c4fffa574e8e4822439c0126f63664577cc6eb59770 | 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: Alexander Bentkamp, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Convex.Between
public import Mathlib.Analysis.Normed.Affine.AddTorsor
public import Mathlib.Analysis.Norm... |
9,971 | lean_file_chunk | 9d6df55d14fc4b7e750bf58424a1598b42c5abf7d4cd41347b329f3154b86512 | 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, Yury Kudryashov
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Analysis.Normed.Group.Add... |
7,483 | lean_file_chunk | ddf4757e16bccb361ea2e87a215d9dd23d29b6dc9723be20add0a1ec0347eb63 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
/-!
# Simplices in torsors over normed spaces... |
23,986 | lean_file_chunk | 5be9ba16e694d036b87038023e3b8931fa5012faa049530e7d406f24e72fb1dd | 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
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.Analysis.Normed.Module.Basic
publ... |
1,362 | lean_file_chunk | 780363f4550e5b943be3428d1e4304f3f0c22ad0399b19069bccb9e1a95c92a6 | lean_source_file | pkg_mathlib_source_file_chunks | { Equiv.Set.image _ (E : Set P₁) hφ with
linear :=
(E.direction.equivMapOfInjective φ.linear (φ.linear_injective_iff.mpr hφ)).trans
(LinearEquiv.ofEq _ _ (AffineSubspace.map_direction _ _).symm)
map_vadd' := fun p v => Subtype.ext <| φ.map_vadd p v }
/-- Restricts an affine isometry to an affine ... |
6,543 | lean_file_chunk | 905fbed814746d6491e6120d271f27ccaa122a576d014800fce3d1b3d8bdf913 | 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.Topology.Instances.RealVectorSpace
public import Mathlib.Analysis.Normed.Affine.Isometry
/-!
# Mazur-Ulam Theorem
Mazur-Ulam theorem... |
6,477 | lean_file_chunk | 1afbc8c3ca2f9b65ac5ffc281c5eb639fa875fe736679a476f3db7ae2377c841 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional
/-!
# Bases in normed affine spaces.... |
3,384 | lean_file_chunk | 9e8c67ea781690b1466d815fc88161d8d8eb366ccbdded6424ccb11579ee6002 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Attila Gáspár. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Attila Gáspár
-/
module
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.Topology.Algebra.AsymptoticCone
/-!
# Asymptotic cones in normed spaces
In ... |
2,097 | lean_file_chunk | f461ca73e23117a50f153d7207003122516933b3280c029a6f98239d6b09343d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Normed.Affine.AddTorsor
public import Mathlib.LinearAlgebra.AffineSpace.Ceva
/-!
# Ceva's theorem.
This file proves various versi... |
6,407 | lean_file_chunk | 8332f2c0d08d02f4fd83e5166a98730f81f0928d893c7b65c3e2a8744865bfce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.Topology.Algebra.ContinuousAffineMap
public import Mathlib.Analysis.Normed.Operator.NormedSpace
public import Mathlib.Analysis.Normed.Group.Ad... |
1,209 | lean_file_chunk | fadbf962a06120bccc90a2e493c3134b292aee0b9cd86c967b9e815e2d1e86f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.GroupTheory.OrderOfElement
public import Mathlib.Algebra.Group.AddChar
public import Mathlib.Algebra.Group.TypeTags.Fini... |
1,448 | lean_file_chunk | b4c9ce9aaabe59174b3966c2955122dde9f2abed6201c2ffe88e3bee252450ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Analysis.Normed.Ring.Lemmas
/-!
# The integers as normed ring
This file contains basic facts about the integers as normed ring.
Recal... |
10,335 | lean_file_chunk | f51d9dd42cf2cfe17c5029feaea5cf7be24ecf66060667a044e6f24a739af4fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Finset
public import Mathlib.Analysis.Normed.Group.Bounded
public import Mathlib.Analysis.No... |
8,930 | lean_file_chunk | 9bfe6792f924bb00fc5cbd4048706d62a517c6ef2194691f7a75ef5350a0012f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Normed.Group.InfiniteSum
public import Mathlib.Topology.Algebra.InfiniteSum.Real
public import Mathlib.Analysis.Normed.Ring... |
1,086 | lean_file_chunk | b08eb3c1de6454f7ab26f6b0569543565414360001a7c227f90f8cf598ad02fa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Algebra.Group.TransferInstance
public import Mathlib.Algebra.Ring.TransferInstance
public import Mathlib.Analysis.Normed.Ring.Basi... |
2,510 | lean_file_chunk | a902241d426e97a834806f68d92cb901595f55e020e8c6a436e021c3348a3c7d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Analysis.Normed.Ring.Basic
public import Mathlib.Analysis.Normed.Group.Ultra
/-!
# Ultrametric norms on rings where the norm of one i... |
23,948 | lean_file_chunk | 421ff7755c000ed3d8deefbb8c3a2998e240bfeb01baac71421f373da643ca28 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Algebra.Algebra.Subalgebra.Basic
public import Mathlib.Analysis.Normed.Group.Constructions
public import Mathlib.Analysi... |
17,113 | lean_file_chunk | 2b2388cf8dee00e637a60b93328663cd40debdc35e54171d476a4a7d10ef2db1 | lean_source_file | pkg_mathlib_source_file_chunks | commutative ring, with the restriction of the norm. -/
instance NonUnitalSubalgebra.nonUnitalNormedCommRing {𝕜 : Type*} [CommRing 𝕜] {E : Type*}
[NonUnitalNormedCommRing E] [Module 𝕜 E] (s : NonUnitalSubalgebra 𝕜 E) :
NonUnitalNormedCommRing s :=
{ s.nonUnitalSeminormedCommRing, s.nonUnitalNormedRing with... |
12,066 | lean_file_chunk | 666cab806f277c88fc74a87cd498fd390eafebff683e72af0c42bc5dd155e5b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.Algebra.Algebra.TransferInstance
public import Mathlib.Algebra.Module.TransferInstance
public import Mathlib.Analysis.Normed.Ring.... |
2,277 | lean_file_chunk | e4521d0811f36dd027c135e724950dadc4d167417d6b133d216849573323e659 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Summable
public import Mathlib.Analysis.Normed.Group.Tannery
/-!
# Infinite products in normed rings
Thi... |
10,516 | lean_file_chunk | e7f1f22ac58986817ba84854fc2e79898b3a13945d73bc21f09a28ec3692e666 | 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.Analysis.SpecificLimits.Normed
public import Mathlib.Topology.Algebra.Ring.Ideal
public import Mathlib.RingTheory.Ideal.Nonunits
/-!
... |
12,262 | lean_file_chunk | fb869c211b008ddb62f00cd5e1cc7fd7c640617e797799608da57c8daa0a5c5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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
-/
module
public import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
/-!
# SeminormFromConst
In this file, we prove [BGR, Propositi... |
6,467 | lean_file_chunk | 65af39b7bb79ae6c92996a06335ff06ace1bd5456908d46521f709700e126584 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 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
-/
module
public import Mathlib.Analysis.Normed.Group.Ultra
public import Mathlib.Analysis.Normed.Unbundled.FiniteExtension
public impor... |
23,973 | lean_file_chunk | 3440e823e53af8873bd493e63638b08c3331b4737586691406e2f98be3d69d65 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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
-/
module
public import Mathlib.Algebra.Order.GroupWithZero.Bounds
public import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
public i... |
8,801 | lean_file_chunk | b11778ff172c6823a807594aab6ac04ff3ae2fcd150096ef90947a024a984de9 | lean_source_file | pkg_mathlib_source_file_chunks | have h_bdd : IsBoundedUnder LE.le atTop fun n : ℕ => μ (y ^ nu (ψ n)) ^ (1 / (ψ n : ℝ)) :=
RingSeminorm.isBoundedUnder μ hμ1 hnu_le ψ
apply le_trans hxy' (mul_le_mul hx hy (le_limsup_of_frequently_le (Frequently.of_forall
(fun n ↦ by positivity)) h_bdd) (rpow_nonneg (smoothingFun_nonneg μ hμ1 x) _))
a... |
4,701 | lean_file_chunk | 1f1d5e9b88e3d7d8c8480425c1ee010f984e12e3b40e8850dc670809fcbcc5e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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
-/
module
public import Mathlib.Analysis.Normed.Unbundled.AlgebraNorm
public import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
/-... |
23,978 | lean_file_chunk | d3b35987a5431b5219628854c6c9f55aa563138040128294638eb2aa6a781751 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps
public import Mathlib.Analysis.Normed.Unbundled.InvariantExte... |
23,944 | lean_file_chunk | 10ac74c599cb77026346472668f90647034dcf6d7e788fd426fe65faa485c0c8 | lean_source_file | pkg_mathlib_source_file_chunks | (exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional h_fin hna)).2.2
rw [spectralNorm_eq_iSup_of_finiteDimensional_normal K L hf_pow hf_na hf_ext]
simp only [invariantExtension_apply, algNormOfAlgEquiv_apply, hf]
/- Note that the main results below are reproved without the finite dimensionality and normali... |
832 | lean_file_chunk | e0cfe655c0d102a49bb6a843bf85abb1f2a7799f9f5ebfd7cc66b0d632e065b1 | lean_source_file | pkg_mathlib_source_file_chunks | have : Algebra.IsAlgebraic K E := Algebra.IsAlgebraic.trans K L E
rw [one_div, Real.eq_rpow_inv (spectralNorm_nonneg x) (norm_nonneg ((minpoly K x).coeff 0)),
Real.rpow_natCast, @spectralNorm.eq_of_tower K _ E,
← @spectralNorm_extends K _ L _ _ ((minpoly K x).coeff 0),
@spectralNorm.eq_of_tower K _ E _ _ ... |
8,719 | lean_file_chunk | 1d40a416e66a7b37fe3aeb40c5f7b91f76f0c8c3cc898a65784f415ac4328cc2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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
-/
module
public import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
public import Mathlib.Analysis.Seminorm
/-!
# Algebra norms
We ... |
12,328 | lean_file_chunk | b8a142d5e397f9d40de8b48d4bb43768fcbf0d15afb299e9a2598580c0366dd7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
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
-/
module
public import Mathlib.Analysis.Normed.Unbundled.AlgebraNorm
public import Mathlib.Analysis.Normed.Unbundled.SeminormFromBounde... |
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