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 |
|---|---|---|---|---|---|
16,589 | lean_file_chunk | ee75dc90f94c64c4ca0f8209ad167e95475abce16cd8b62ad50323252bc7806c | 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.Continuous
/-!
# Linear maps on inner product spaces
This file studies li... |
4,836 | lean_file_chunk | becbe6bc4af7ef82a6e4f998687f68e82f4a14c9daacbf5eb46b35e393ca6fa9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Peter Pfaffelhuber. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Pfaffelhuber
-/
module
public import Mathlib.Analysis.InnerProductSpace.Basic
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.LinearAlgebra.Matri... |
18,974 | lean_file_chunk | 3e021fd9e6039947b4b921529160f4236befa50abd73e7624c8d35d3b8c3e1b4 | 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.Subspace
public import Mathlib.LinearAlgebra.SesquilinearForm.Basic
public ... |
4,932 | lean_file_chunk | 41d00c0d6c40d69328c34d425f219da316088b237926f1692dc98fda8cc775ac | 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.Basic
public import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps
/-!... |
5,754 | lean_file_chunk | 28fc387cad245f021ed304ed48ed38191351cfd995920b7084f5b518b2982901 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
module
public import Mathlib.Analysis.InnerProductSpace.Calculus
public import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
/-!
# Properties abo... |
8,746 | lean_file_chunk | a955d28c85f391737d27f8f3daf02ed4af04a10530a9553af4ce8c0b3b0cb388 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.PiL2
public import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
public import Mathlib.Analysis.N... |
12,390 | lean_file_chunk | 6440570405ce053cb6168383f0c7e84871042a228cd9f201e9d42703eef6e2cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.InnerProductSpace.Adjoint
public import Mathlib.Analysis.InnerProductSpace.ProdL2
public import Mathlib.Analysis.Normed.Operator.Exte... |
15,217 | lean_file_chunk | 06cb83e0e50c072cec23d08e43d3e44a2255b8e1746ae19a7ff6546ac0d52cab | 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: Moritz Doll, Frรฉdรฉric Dupuis, Heather Macbeth
-/
module
public import Mathlib.Analysis.InnerProductSpace.Subspace
public import Mathlib.Analysis.Normed.Operator.Banach
public import... |
2,755 | lean_file_chunk | 51cccb39f702fa065f750a0a715f07f40ae75f197f2d91b78af1900f452b5d7e | 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.InnerProductSpace.PiL2
/-!
# Canonical tensors in real inner product spaces
Given an `InnerProductSpace โ E`, this file defin... |
5,256 | lean_file_chunk | 77ba834e36878a71e03c96f750457a9cf52ea1bcea49ecf2a231d7a82d34d0b7 | 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
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
public import Mathlib.Analysis.Normed.Lp.ProdLp
/-!
# `Lยฒ` inner product space structure on products of inner... |
3,883 | lean_file_chunk | dc8b9a0b294cb928aed4f83f4f0e2519e29c503050b629b8a7b49b3926f4b184 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.InnerProductSpace.Basic
public import Mathlib.Analysis.Normed.Group.AddTorsor
/-!
# Normed affine spaces over an inner product space
... |
1,539 | lean_file_chunk | 2be0160fa4d20615acf5c669af69cdb318336cf0be5dd3135af8a73f4f4e171f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.InnerProductSpace.Projection.Submodule
public import Mathlib.LinearAlgebra.Semisimple
/-!
# Semisimple operators on inner product sp... |
23,442 | lean_file_chunk | dc31bbf567551c86fe75e4ffcae4bd51f24aefd2583e86ba125214e5d3aa9c9c | 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.InnerProductSpace.Rayleigh
public import Mathlib.Analysis.Normed.Group.Submodule
public import Mathlib.Analysis.Normed.Operat... |
586 | lean_file_chunk | bcf0ef68dc759cd527a73b8a0276a7b60113a9476b96c60633b37d61020c1983 | 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.CStarAlgebra.Classes
public import Mathlib.Analysis.InnerProductSpace.Adjoint
/-! # `E โL[โ] E` as a Cโ-algebra
We place this h... |
9,226 | lean_file_chunk | d197471d3138e0e62d514c421870a7a60943d6e586d6a27b930a29a149db767e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Algebra.Exponential
public import Mathlib.Analysis.CStarAlgebra.Classes
import Mathlib.Analysis.CStarAlgebra.ContinuousFun... |
13,218 | lean_file_chunk | ab27835da75d49f0e94be34c0f4d9cc2607e0bcd00e60b40f4d528a8d66a4721 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Hans Parshall. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hans Parshall
-/
module
public import Mathlib.Analysis.InnerProductSpace.Adjoint
public import Mathlib.Analysis.Matrix.Normed
public import Mathlib.Analysis.RCLike.Basic
public import ... |
6,108 | lean_file_chunk | 69f4692115716f2ea094d08f538ce76d6dfa3a4a83223d6f665b0fece98709f0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Frรฉdรฉric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Algebra.Order.Module.PositiveLinearMap
public import Mathlib.Analysis.CStarAlgebra.Classes
public import Mathlib.Analysis.CStarAlgebra... |
7,911 | lean_file_chunk | 2ab51671f7b88edb9be57b1a062490451c7cf668f049c81bf8f515ef3c730a9f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Gregory Wickham. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gregory Wickham
-/
module
public import Mathlib.Analysis.CStarAlgebra.PositiveLinearMap
public import Mathlib.Analysis.InnerProductSpace.Adjoint
public import Mathlib.Analysis.InnerP... |
6,317 | lean_file_chunk | 9b915399cbb30e6d94fc347df9360ce9f15b3806df455396367c8f51ff6597ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.CStarAlgebra.PositiveLinearMap
public import Mathlib.Analysis.CStarAlgebra.CStarMatrix
/-! # Completely positive maps
A lin... |
2,306 | lean_file_chunk | 9c5359ea7280c85b3af5883d7e337dd3758330429b0f426141b68d90059d5c40 | 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.Algebra.Exponential
/-! # The exponential map from selfadjoint to unitary
In this file, we establish various properties r... |
10,562 | lean_file_chunk | 6b9781d39224ba8da4d94eed362dbebe3802bfef89b431c668c5d431f7dd806c | 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
-/
module
public import Mathlib.Analysis.Normed.Group.Hom
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Analysis.Normed.Operator.LinearIsom... |
15,337 | lean_file_chunk | 48e6b8de899ddc492070cd66aec5d7294545631f46432cf99ca0ad5d94c4e40f | 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.CStarAlgebra.ContinuousFunctionalCalculus.Order
public import Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart
public impor... |
1,589 | lean_file_chunk | 1be214e3b4cf7adb7bf7987ae3f24f68e0f6b55f564acf2332df09e7f1c9ffab | 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.CStarAlgebra.Classes
public import Mathlib.Topology.ContinuousMap.Compact
public import Mathlib.Topology.ContinuousMap.ZeroAtInft... |
1,259 | lean_file_chunk | 4d3157ebbcbea36b3c256c5aed0ec30cfe502d18766419cd010a1af73206c404 | 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.CStarAlgebra.Classes
public import Mathlib.Analysis.Normed.Lp.lpSpace
/-! # `lp โ A` as a Cโ-algebra
We place these here becaus... |
23,955 | lean_file_chunk | a768949926590d9e91029575e9eaed6dfb7a5992d950276864571d2635a9b715 | 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, Jon Bannon
-/
module
public import Mathlib.Analysis.CStarAlgebra.Unitization
public import Mathlib.Analysis.CStarAlgebra.Classes
public import Mathlib.Analysis.SpecialFu... |
942 | lean_file_chunk | c0c693d4a57a14c33d95ed267af65da6e29f109769d73d48dcdce892c150fea3 | lean_source_file | pkg_mathlib_source_file_chunks | ยท simp only [Set.mem_image, exists_exists_and_eq_and]
have hr' : NNReal.sqrt r < โaโโ := โaโโ.sqrt_mul_self โธ NNReal.sqrt_lt_sqrt.2 hr
simp_rw [โ nnnorm_fst, โ sSup_unitClosedBall_eq_nnnorm] at hr'
obtain โจ_, โจx, hx, rflโฉ, hxrโฉ := exists_lt_of_lt_csSup (hball.image _) hr'
have hx' : โxโโ... |
9,226 | lean_file_chunk | f89dfe10bcc5e2c3fb5e94f4ce7341705cc207860335137764db350b527231d7 | 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.CStarAlgebra.Classes
public import Mathlib.Analysis.Normed.Algebra.Unitization
/-! # The minimal unitization of a Cโ-algebra
Thi... |
5,612 | lean_file_chunk | bc8faafefc1a626a80100aa1bb59844b8b63039f63695de885b239ab6d606808 | 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.Complex.Basic
public import Mathlib.Topology.Algebra.NonUnitalStarAlgebra
public import Mathlib.Topology.Algebra.StarSubalgebra
... |
12,814 | lean_file_chunk | a46d6589383b84b15fa3e5af64b99d690e2bd81d7cc540a31cc25fae34a84ca6 | 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.CStarAlgebra.Spectrum
public import Mathlib.Analysis.CStarAlgebra.ContinuousMap
public import Mathlib.Analysis.Normed.Group.Quoti... |
23,917 | lean_file_chunk | b67eec428c2dc4be3b646db3d2bb6170d4956d078501ba6e77d319336a7c8ab7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.CStarAlgebra.Module.Constructions
public import Mathlib.Analysis.Matrix.Normed
public import Mathlib.Topology.UniformSpace.Ma... |
10,366 | lean_file_chunk | b71fed91b0e75972574e277231e75b2df50a309e1e930945e57e331e9bbdb216 | lean_source_file | pkg_mathlib_source_file_chunks | norm_triangle Mโ Mโ := by simpa [โ map_add] using norm_add_le (toCLM Mโ) (toCLM Mโ)
norm_eq_zero_iff := by
simpa only [norm_def, norm_eq_zero, โ injective_iff_map_eq_zero'] using toCLM_injective
open WithCStarModule in
lemma norm_entry_le_norm {M : CStarMatrix m n A} {i : m} {j : n} :
โM i jโ โค โMโ := by
c... |
4,962 | lean_file_chunk | 16ffb516c4274ae9ae9575f781f64aef8edebbdb77ef9cdef960887fbeeab5a5 | 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, Jireh Loreaux
-/
module
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCa... |
3,935 | lean_file_chunk | 3dd40567bbef8fb7baeff986740ab4a4f7f0f2144147472b1e6a5666651a274b | 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.CStarAlgebra.ContinuousFunctionalCalculus.Order
/-! # Properties of Cโ-algebra homomorphisms
Here we collect properties of Cโ-a... |
14,386 | lean_file_chunk | 9e95e9c214f374acc52b5c477436d305ac70d31ea0cea903d419348ac9ddc260 | 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.CStarAlgebra.Unitization
public import Mathlib.Analysis.Complex.Convex
public import Mathlib.Analysis.Normed.Algebra.GelfandFormu... |
23,972 | lean_file_chunk | 0e013388b35950bbc73821bc20f6e7dcaa133eb97e0765f5b8cc3bea696ed03f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Pi
public import Mathlib.Analysis.InnerProductSpace.EuclideanDist
public import Mathlib.Ana... |
12,305 | lean_file_chunk | c056b74f7bc6c74fffe910d58a7041eab44acd1c5c424d95bc674a85e312c677 | lean_source_file | pkg_mathlib_source_file_chunks | Then the `Lแต'` norm of `u` is bounded above by a constant times the `Lแต` norm of
the Frรฉchet derivative of `u`.
Note: The codomain of `u` needs to be a Hilbert space.
-/
theorem eLpNorm_le_eLpNorm_fderiv_of_eq_inner {u : E โ F'}
(hu : ContDiff โ 1 u) (h2u : HasCompactSupport u)
{p p' : โโฅ0} (hp : 1 โค p) (hn : ... |
5,653 | lean_file_chunk | ceb0e9893fbaf96333a3befc16250905264a3b959d0b98c903db142b2845c883 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.SpecialFunctions.Pow.Complex
import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Mathlib.LinearAlgebra.Basis.VectorSpace... |
3,823 | lean_file_chunk | ba59ecb6ff3669bbe8add1492ed67435b8f9d83aaaf10b60877fc9b7da812ebb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Normed.Module.FiniteDimension
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Topology.Instances.RealVector... |
7,382 | lean_file_chunk | 059352ef25b905e6d3b74c3561bd752d495cd3eeba96508b7eef52a1522433b5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaรซl Dilies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaรซl Dilies
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# L2 inner product of finite sequences
This file defines the weighted L2 inner product of functions `f g... |
23,967 | lean_file_chunk | f0beb495222c55367d469f7ab135afdf121b2925ee25433cc1044509b61762d3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Frรฉdรฉric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frรฉdรฉric Dupuis
-/
module
public import Mathlib.Algebra.Algebra.IsSimpleRing
public import Mathlib.Algebra.BigOperators.Balance
public import Mathlib.Algebra.Order.BigOperators.Expec... |
22,751 | lean_file_chunk | b5332e90203b75f1001e1bd731ecf8125a118afce1980904ddb51547ac22c383 | lean_source_file | pkg_mathlib_source_file_chunks | theorem re_eq_self_of_le {a : K} (h : โaโ โค re a) : (re a : K) = a := by
rw [โ conj_eq_iff_re, conj_eq_iff_im, im_eq_zero_of_le h]
open IsAbsoluteValue
theorem abs_re_div_norm_le_one (z : K) : |re z / โzโ| โค 1 := by
rw [abs_div, abs_norm]
exact div_le_one_of_leโ (abs_re_le_norm _) (norm_nonneg _)
theorem abs_i... |
7,059 | lean_file_chunk | d5f25c35e1c95566e57ba008dae63fc3def8154ed8899945b95a3fb23ae0090e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
module
public import Mathlib.Algebra.Algebra.RestrictScalars
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.LinearAlgebra.Dual.Defs
/-!
#... |
2,148 | lean_file_chunk | f18b44b75ac23e10544610413cb387d27eeb3eb676caf2b79246294206fbccca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jakob Stiefel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Stiefel
-/
module
public import Mathlib.Algebra.Algebra.Subalgebra.Tower
public import Mathlib.Analysis.Normed.Operator.NNNorm
public import Mathlib.Analysis.RCLike.Basic
public ... |
1,809 | lean_file_chunk | 9a82ba84b053da33d116aeb1df47167292bc2d9135b4a7c23dc7f84752c7f026 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sรฉbastien Gouรซzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sรฉbastien Gouรซzel
-/
module
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Topology.Instances.RealVectorSpace
public import Mathlib.Analysis.Calculus.TangentCone... |
6,724 | lean_file_chunk | ed87baa1802bb5be538ff94b861cc1fe38f1d188b4c853255ba1d129d762b20a | 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
-/
module
public import Mathlib.Analysis.CStarAlgebra.Classes
public import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# Von Neumann algebras
We give the "abstract" a... |
15,618 | lean_file_chunk | aba0e1853b91a227a0a510ae4b518d2f6740e88ee31e1aa8d70032bee842ada4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Ian Jauslin and Alex Kontorovich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ian Jauslin, Alex Kontorovich, Oliver Nash
-/
module
public import Mathlib.Analysis.Complex.CauchyIntegral
public import Mathlib.Analysis.Complex.Convex
/-!
# Primi... |
6,431 | lean_file_chunk | 00df03561c3d8e78a5f3d536d6e4b6b91dc9757f8f233cdc2af0283fd5dd6fb3 | 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.Complex.Basic
public import Mathlib.Analysis.RCLike.Lemmas
public import Mathlib.Topology.TietzeExtension
public import Mathlib.A... |
4,943 | lean_file_chunk | 3c7b714bd2e0ee7f9430608319fa1bd327717042fcb470265550aa82749a14e2 | 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, Yaรซl Dillies
-/
module
public import Mathlib.Analysis.Complex.ReImTopology
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.Pa... |
2,371 | lean_file_chunk | 33e089fbb2646ef9cee33665b43ba34b9c7347b9c8bcddc015817cc03df74290 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sรฉbastien Gouรซzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sรฉbastien Gouรซzel
-/
module
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.Analysis.Normed.Operator.NormedSpace
public import Mathlib.LinearAlgebra.Complex.Dete... |
15,166 | lean_file_chunk | 0a8ba0fb7b371f4d7b7d157881eb088f167c1ca588a9407feb131c2bd6100f5e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
module
public import Mathlib.Analysis.Analytic.IsolatedZeros
public import Mathlib.Analysis.Analytic.Polynomial
public import Mathlib.Analysis.Complex.AbsMax
publi... |
3,171 | lean_file_chunk | ce937f1b44656013705efeedba035956cdb189e645cc1684119435ba52cfd4a8 | 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: Mario Carneiro, Joseph Myers
-/
module
public import Mathlib.Analysis.Complex.Exponential
public import Mathlib.Analysis.SpecialFunctions.Log.Deriv
/-!
# Bounds on specific values of t... |
2,556 | lean_file_chunk | a2866d8ba3939e8acd73d10f0a23d0632f360d71da60a067b58af0b79e643318 | 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.Analysis.Complex.Basic
public import Mathlib.Analysis.Asymptotics.Theta
/-!
# Lemmas about asymptotics and the natural embedding `โ โ... |
23,947 | lean_file_chunk | 215f3093c84a164e2ba5b54828cce052295d98a04a12ff5742d25142a0a4b623 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Xavier Gรฉnรฉreux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Gรฉnรฉreux
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
public import Mathlib.Analysis.Complex.PhragmenLindelof
/-!
# Hadamard three-lines Theorem
In th... |
6,151 | lean_file_chunk | aee7f75ed839491a5ba91aa32a612896bf4e2784ce7d6ef7a82bdd58f4fc285d | lean_source_file | pkg_mathlib_source_file_chunks | apply (norm_le_interpStrip_of_mem_verticalClosedStripโโ f hz hd hB).trans (this.trans _)
apply mul_le_mul_of_nonneg _ _ (Real.rpow_nonneg (sSupNormIm_nonneg f _) _)
ยท apply (Real.rpow_nonneg _ _)
specialize hb 1
simp only [mem_preimage, one_re, mem_singleton_iff, forall_true_left] at hb
exact (norm_nonn... |
5,639 | lean_file_chunk | 1c7c7a591e44a049faea24c2f6821d9e8e40a06830d57f11d9f2a2578d5dffd1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Maksym Radziwill. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maksym Radziwill
-/
module
public import Mathlib.Analysis.Complex.Schwarz
/-!
# Borel-Carathรฉodory theorem
This file proves the Borel-Carathรฉodory theorem: for any function `f` a... |
5,346 | lean_file_chunk | d0012365eed07fa169764063a0e5a29f1d8859d604cc5cc30a8fef13d413ad8e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Meromorphic.FactorizedRational
/-!
# Canonical Decomposition
If a function `f` is meromorphic on a compact set `U`, then it h... |
6,292 | lean_file_chunk | 5407eb98a183e294a2d89baa919f85bd02ab3d31cceada2eb9ab6a08a9a84291 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.CauchyIntegral
/-!
# Convergence of Taylor series of holomorphic functions
We show that the Taylor series around some p... |
6,913 | lean_file_chunk | c096b2486f44418c5b30b62ec143cd617afbb52df0aac9d598ce1afb8b9308ab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Franรงois Sunatori. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Franรงois Sunatori
-/
module
public import Mathlib.Analysis.Complex.Circle
public import Mathlib.LinearAlgebra.Determinant
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGr... |
4,537 | lean_file_chunk | 3ec7d2991cfff4ff4f48e388996b1fb2566e99ee020168b71d486dce6e6506a6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaรซl Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaรซl Dillies
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds
public import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic
/-!
# Angle between complex ... |
14,481 | lean_file_chunk | 69b717d412aa5321fa15fb1abc0e5a12e931004dd4d49ac187b4ee3f754bcf5b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sรฉbastien Gouรซzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sรฉbastien Gouรซzel
-/
module
public import Mathlib.Analysis.Normed.Group.Real
public import Mathlib.Data.Complex.Basic
public import Mathlib.Data.Real.Sqrt
/-!
# Norm on the comp... |
9,064 | lean_file_chunk | 89d431ffd6a708340da3f24dc868d9c4965462ee6b6389c060244adf7be76dea | 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.Calculus.FDeriv.Analytic
public import Mathlib.Analysis.Asymptotics.SpecificAsymptotics
public import Mathlib.Analysis.Comple... |
2,574 | lean_file_chunk | ad222cf2109fe2b2bf716d03f33d4d0c8136386f9825d1900b707d64ab1df25e | 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.RCLike.Sqrt
public import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
/-!
# Derivatives of `Complex.sqrt`
This file proves th... |
23,001 | lean_file_chunk | fd349adda3d34074ba0f78e95b0c01551771266c1961172681c1cfb5961b5896 | 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.Complex.CauchyIntegral
public import Mathlib.Analysis.InnerProductSpace.Convex
public import Mathlib.Analysis.Normed.Affine.A... |
8,782 | lean_file_chunk | c91241c18f739210c680e5ca1411d8f0c17b2ee4a410d47b884694004deb8b53 | 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.Complex.Basic
public import Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle
/-!
# Closure, interior, and frontier o... |
23,931 | lean_file_chunk | 5a3875a74c875b2db88516854fc1059a8e10d1b9014f5872c7ae31dd1ea69a04 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Analysis.Complex.Norm
public import Mathlib.Algebra.Order.CauSeq.BigOpera... |
2,817 | lean_file_chunk | c85d9f4032ddf196fd8e3c833f8d65964f972bbc1f61c06878386dbd51106e03 | lean_source_file | pkg_mathlib_source_file_chunks | -- (It may also need the positivity extensions in https://github.com/leanprover-community/mathlib4/pull/3907.)
rw [show 3 = 1 + 1 + 1 from rfl]
repeat rw [Finset.sum_range_succ]
norm_num [Nat.factorial]
nlinarith
_ < 1 / (1 - x) := by rw [lt_div_iffโ] <;> nlinarith
theorem exp_bound_div_one... |
5,726 | lean_file_chunk | 247944e26558d445d2645b110499adc1734cfdcef2b7b8414c6367f2abf3956d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Analysis.Complex.Norm
/-!
# The partial order on the complex numbers
This order is defined by `z โค w โ z.re โค w.re โง z.im = w.im`.
This i... |
2,177 | lean_file_chunk | 8ca7be160b5e53928e483f31831eb55ebca462ce45ad664771a96ce5338a025d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
module
public import Mathlib.Analysis.InnerProductSpace.Convex
public import Mathlib.Analysis.SpecialFunctions.Complex.Arg
/-!
# Rays in the complex numbers
This f... |
2,467 | lean_file_chunk | e2b3823bca29809706679ff1fca79e2dbd98ebafa83bf5fdd54b70b26e8e0c35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Complex.UpperHalfPlane.Basic
/-!
# Integer Complement
We define the complement of the integers in the complex plane and give ... |
1,638 | lean_file_chunk | 427f0aca36cb7bb94a7303ccef43f6606d4bf26135cd7c32babaab2b1024795f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.Topology.Instances.EReal.Lemmas
/-!
# Half-planes in โ are open
We state that open left, ri... |
23,974 | lean_file_chunk | 7e9929303316e27f20d7bcd001c55368891f9af61c5ea914229c6638835b67c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sรฉbastien Gouรซzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sรฉbastien Gouรซzel
-/
module
public import Mathlib.Analysis.Complex.Order
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Data.Complex.BigOperators
public import M... |
2,112 | lean_file_chunk | 32e2d1a4f01b2b3cd2b9981a94469ef1b40d843818f33daf19b50223b9726fb1 | lean_source_file | pkg_mathlib_source_file_chunks | mem_slitPlane_iff_not_le_zero.symm
lemma slitPlane_ne_zero {z : โ} (hz : z โ slitPlane) : z โ 0 :=
ne_of_mem_of_not_mem hz zero_notMem_slitPlane
/-- The slit plane includes the open unit ball of radius `1` around `1`. -/
lemma ball_one_subset_slitPlane : Metric.ball 1 1 โ slitPlane := by
intro z hz
apply Or.inl... |
10,252 | lean_file_chunk | 4c105c725157a0105358c899bc1bfc0ce43acaba954839191a11d627ae0f1b8a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
module
public import Mathlib.Analysis.Complex.RemovableSingularity
public import Mathlib.Analysis.Calculus.UniformLimitsDeriv
public import Mathlib.Analysis.Normed... |
1,002 | lean_file_chunk | 28233dcce10ff35d79b6053b78d6e5e59a10f807983753ecfd8113c31711e9cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Violeta Hernรกndez Palacios. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Violeta Hernรกndez Palacios
-/
module
public import Mathlib.Analysis.Real.Cardinality
public import Mathlib.Data.Complex.Basic
/-!
# The cardinality of the complex numbers... |
734 | lean_file_chunk | e9b5cc314876115ecaa3afd6725a572bfcb73471a85affe78172901e691f39ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yuyang Zhao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuyang Zhao
-/
module
public import Mathlib.Algebra.Algebra.Rat
public import Mathlib.Data.Complex.Basic
public import Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic
/-!
# Integral... |
23,999 | lean_file_chunk | 73571e21b54c6f7928d86b13da057b027fc0bb91833ca1f758a0a01bddde123a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir
-/
module
public import Mathlib.Analysis.Complex.Exponential
import Mathlib.Tactic.NormNum.NatFactorial
/-!
# Trigonometric and hyperbolic trigon... |
10,490 | lean_file_chunk | 8706634df98a7d83f216ac87d812541bd047a3b29318b14590d85a645a53f032 | lean_source_file | pkg_mathlib_source_file_chunks | rw [sin_sq, cos_sq, โ sub_sub, sub_half]
theorem abs_sin_eq_sqrt_one_sub_cos_sq (x : โ) : |sin x| = โ(1 - cos x ^ 2) := by
rw [โ sin_sq, sqrt_sq_eq_abs]
theorem abs_cos_eq_sqrt_one_sub_sin_sq (x : โ) : |cos x| = โ(1 - sin x ^ 2) := by
rw [โ cos_sq', sqrt_sq_eq_abs]
theorem one_add_tan_sq_mul_cos_sq_eq_one {x : โ... |
12,737 | lean_file_chunk | 2c2771563ee5e7d2109bbcd0e78a8b07f7f6c55ee8ef2286e419d5735c040a96 | 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.SpecialFunctions.Integrals.PosLogEqCircleAverage
import Mathlib.Algebra.FiniteSupport.Basic
/-!
# Jensen's Formula of Complex... |
23,942 | lean_file_chunk | 6a081fc168058837362965d8b1a914e7352e5667840eba27980313ebba840a40 | 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.Analytic.Uniqueness
public import Mathlib.Analysis.Calculus.DiffContOnCl
public import Mathlib.Analysis.Calculus.DSlope
publi... |
19,866 | lean_file_chunk | 0ba8df7226a35c1e7501c3f8be011db38fb484fc11017a97cba3f77794ffa5e1 | lean_source_file | pkg_mathlib_source_file_chunks | **Cauchy integral formula** for the value at the center of a disc. If `f : โ โ E` is continuous on a
closed disc of radius `R` and center `c`, and is complex differentiable at all but countably many
points of its interior, then the integral $\oint_{|z-c|=R} \frac{f(z)}{z-c}\,dz$ is equal to
`2ฯi โข f c`.
-/
theorem circ... |
5,578 | lean_file_chunk | 67e8a2ce99fcc536f892df64557d45a1ef9ccbe04733bc66e07be8a157b27265 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Polynomial
public import Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv
public import Mathlib.Analysis.SpecialFunction... |
3,551 | lean_file_chunk | b9b49a271c328cc87da60d6bcc9dfe87c19fbfbbae5fa0b1b15cb6a36a8a8529 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.TaylorSeries
/-!
# Nonnegativity of values of holomorphic functions
We show that if `f` is holomorphic on an open disk ... |
23,993 | lean_file_chunk | adf16c02e8d89b9a99651dd6bb6f35c367b114d390574c8dfa7cd0dc32fe406c | 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.Complex.AbsMax
public import Mathlib.Analysis.Asymptotics.SuperpolynomialDecay
/-!
# Phragmen-Lindelรถf principle
In this fi... |
20,523 | lean_file_chunk | d5c7d4602dd0bacd504208231ed750f9eeb7312e29451fd00d7bb9d28c48726e | lean_source_file | pkg_mathlib_source_file_chunks | change โ(f โ (ยท * I)) zโ โค C
have H : MapsTo (ยท * I) (Ioi 0 รโ Ioi 0) (Iio 0 รโ Ioi 0) := fun w hw โฆ by
simpa only [mem_reProdIm, mul_I_re, mul_I_im, neg_lt_zero, mem_Iio] using hw.symm
rcases hB with โจc, hc, B, hOโฉ
refine quadrant_I (hd.comp (differentiable_id.mul_const _).diffContOnCl H) โจc, hc, B, ?_โฉ him
... |
5,799 | lean_file_chunk | 3aa9bacb5d57205ed35755fb94a34edd921d78169fd332068e82f1ac878a6ab3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sรฉbastien Gouรซzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sรฉbastien Gouรซzel, Yourong Zang
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Operations
public import Mathlib.Analysis.Calculus.Deriv.Linear
public import Mathlib.Ana... |
12,293 | lean_file_chunk | 7b72efb83fe0f758b4b702117d793001d92991e0b5371f9615b7ee9206cc1532 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.RemovableSingularity
public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.Deriv
public import Mathlib.Order.F... |
7,631 | lean_file_chunk | 96e0d5c2c9c47d5a223427d34786ed1adaffee394b94fea4b25e1129f6f34248 | 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.Complex.CauchyIntegral
public import Mathlib.Analysis.Calculus.FDeriv.Analytic
public import Mathlib.Analysis.Normed.Module.C... |
14,224 | lean_file_chunk | af1bb6410633abca0e4884476b6cd3fcfcdb8c8e5d82719ba4ae1ba6bc89be1e | 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, Stefan Kebekus
-/
module
public import Mathlib.Analysis.Calculus.Conformal.NormedSpace
public import Mathlib.Analysis.Calculus.Deriv.Basic
public import Mathlib.Analysis.C... |
1,104 | lean_file_chunk | d9a829eb232a05bfc3384794924909b65e6d3551b564d4a29edf017589aa52f6 | 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.CStarAlgebra.Classes
public import Mathlib.Analysis.Complex.LocallyUniformLimit
public import Mathlib.Topology.Algebra.Infinite... |
12,323 | lean_file_chunk | 403ea184887b68c06686bad6084b20869f3b36a0bf2bcd1e6b8c066a46ee7dc2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
module
public import Mathlib.Analysis.Complex.Basic
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.Tactic.Peel
public import Mathlib.Tactic.Posit... |
5,161 | lean_file_chunk | 380d2ddc467a4ce81434755001021c83c19428a80aeca59d6772a17ce05901d3 | 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.Complex.CauchyIntegral
public import Mathlib.MeasureTheory.Integral.CircleAverage
/-!
# The Mean Value Property of Complex Dif... |
17,560 | lean_file_chunk | 10067c49f6825b24539b6c26a5ba40f959fffb13d36910976c3e233275b12526 | 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.Complex.AbsMax
public import Mathlib.Analysis.Complex.RemovableSingularity
/-!
# Schwarz lemma
In this file we prove severa... |
9,872 | lean_file_chunk | 578167e6409eebb6934e7cccd20fa4444aa96af6755839f93962a208c4b706e7 | 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.SpecialFunctions.Trigonometric.Basic
public import Mathlib.Analysis.Normed.Field.UnitBall
/-!
# The circle
This file define... |
11,715 | lean_file_chunk | 141149794250d03453f24720885141b92e8735715945322c2664c366cc0ac390 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mihai Iancu, Stefan Kebekus, Sebastian Schleissinger, Aristotle AI
-/
module
public import Mathlib.Analysis.Complex.MeanValue
/-!
# Poisson Integral Formula
We present two versions ... |
1,305 | lean_file_chunk | 277822b8300196bd771b7ac47ac07b1c6eb385c6253defa7cdf322094410b7b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
public import Mathlib.Analysis.Complex.Basic
/-!
# Some lemmas on the spectrum and quasispectrum o... |
12,483 | lean_file_chunk | 85e9d5452c7dca04efabb3c7e7978ab0e62c293ae9ac02577971442a5dbf2f61 | 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.Asymptotics.Lemmas
public import Mathlib.Analysis.Normed.Module.Basic
/-!
# Asymptotic equivalence up to a constant
In this... |
23,936 | lean_file_chunk | b574c524b6cc1efbf19c021e02e9dc7d1f2d18a894bbe53462b84569355ce8ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Asymptotics.Defs
public import Mathlib.Analysis.Normed.Group.Bounded
public import Mathlib.Analysis.Normed.Group... |
14,569 | lean_file_chunk | 928cb3835ab4d850ebdcb4967a530188cea9558a190a3329af36f440917eb878 | lean_source_file | pkg_mathlib_source_file_chunks | (h : f =O[๐ xโ] fun x => โx - xโโ ^ n) (hn : n โ 0) : f xโ = 0 := by
rw [โ nhdsWithin_univ] at h
exact h.eq_zero_of_norm_pow_within (mem_univ _) hn
theorem isLittleO_pow_sub_pow_sub (xโ : E') {n m : โ} (h : n < m) :
(fun x => โx - xโโ ^ m) =o[๐ xโ] fun x => โx - xโโ ^ n :=
(isLittleO_pow_pow h).comp_tendst... |
17,526 | lean_file_chunk | a9f5968af5e9f09c61f58c652a82b56241dd059204f4205c9796a70fbc3593ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Asymptotics.Defs
public import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Asymptotics.Theta
/-!
# Asympt... |
1,627 | lean_file_chunk | 45a5986aed2ad2a122a793625dbe96e16f2c8873539714e5b9ead2984c5a9661 | 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.Normed.Group.Completion
public import Mathlib.Analysis.Asymptotics.Defs
public import Mathlib.Topology.Algebra.InfiniteSum.Or... |
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