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 |
|---|---|---|---|---|---|
12,260 | lean_file_chunk | b80065d4e18194ab1072fd2385397d67f5bbe83c5fe46eae65de1bfe6255498f | 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, Jean Lo, Calle Sönne, Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.Arg
public import Mathlib.Analysis.Spec... |
10,928 | lean_file_chunk | c70c2375cec75186c5049cbdbba9be945fc959634005a44189e7dc66ac5dab99 | 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.Complex.Circle
public import Mathlib.Analysis.SpecialFunctions.Complex.Log
public import Mathlib.Topology.Covering.AddCircle
... |
12,109 | lean_file_chunk | d754d9cb997815a0898298ac82920b579dc0376d4987a76a184de6efedc8e5c3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
public import Mathlib.Analysis.SpecialFunctions.NonIntegrable
public import Mathlib.Analys... |
8,643 | lean_file_chunk | 306d89cf1d62472f6b73f3ba23e02f92d4f6b34af4625aac5da775bbf1356407 | 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.Meromorphic.FactorizedRational
public import Mathlib.Analysis.Normed.Module.Connected
public import Mathlib.Analysis.SpecialFun... |
9,897 | lean_file_chunk | db74fd07335701ef1d8987d4751ad2d73bd4b00256dc3d20874e9d3cb3c3c5ae | 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.Harmonic.MeanValue
public import Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions
public import Mathlib.Analys... |
23,995 | lean_file_chunk | 45a3e52af6cb81dda4c0937cd08fd734db7063dd1a013d7eed0a63fdc02e944d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
public import Mathlib.Analysis.SpecialFunctions.NonIntegrable
public import Mathlib.Analys... |
2,972 | lean_file_chunk | bf4b44be4cca374fedc19e10f23fbe7e045a279fd535fd2391298d28f2c44097 | lean_source_file | pkg_mathlib_source_file_chunks | (∫ x in a..b, sin x ^ (2 * m + 1) * cos x ^ n) =
-∫ x in b..a, sin x ^ (2 * m + 1) * cos x ^ n := by rw [integral_symm]
_ = ∫ x in b..a, (↑1 - cos x ^ 2) ^ m * -sin x * cos x ^ n := by
simp only [_root_.pow_succ, pow_mul, _root_.pow_zero, one_mul, mul_neg, neg_mul,
integral_neg, neg_inj]
... |
3,538 | lean_file_chunk | 484a7c90918432c6c9f3ffa11bf75628af00c131858ba975c7aa9199bb6ce421 | 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.Integrability.LogMeromorphic
/-!
# Integral of `log ∘ sin`
This file computes special values of the integral... |
315 | lean_file_chunk | b87c73be919680157f809445632fe112a8f9b8a114c954943f2f2f8e4717c46e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module -- shake: keep-all
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic
deprecated_module (since := "2025-11-15") |
11,442 | lean_file_chunk | f9cfae01c4d03553179b9843c56618098192eba18361910fa09cd11f704d9800 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jon Bannon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Bannon, Jireh Loreaux
-/
module
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunct... |
9,724 | lean_file_chunk | 982315da342f1f03d53a83a8600008e229d95f5b7f78129277b6af08581bd5ce | 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.SpecialFunctions.Complex.LogBounds
public import Mathlib.Topology.Algebra.InfiniteSum.Field
/-!
# Summability of logarithms
W... |
2,550 | lean_file_chunk | ccc04ca8c7ca85267fdb565a60d79443a617c9e11a1450b68b26f4de8f0ceb95 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Alastair Irving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alastair Irving, Michael Stoll
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Deriv
public import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
/-!
# Multiplicat... |
3,789 | lean_file_chunk | 261a48ba00c063b0883284b91dfa6c722cf660c06264f17812cc076ec0f88fb3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Analysis.Complex.Exponential
public import Mathlib.Data.EReal.Basic
/-!
# Extended Nonnegative Real Exp... |
18,760 | lean_file_chunk | 38a8a3abc02c7e0a11f51ecb3ce35cb512d0335b3b2edc77065b116361635c29 | 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, Jean Lo, Calle Sönne
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Pow
public import Mathlib.Analysis.Calculus.LogDeriv
public import M... |
23,996 | lean_file_chunk | 26962ecf43d62dfbcfb85ad9a9ac52db27584d2177428db89854a2770d9fd7a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey, Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Analysis.SpecialFunctions.P... |
171 | lean_file_chunk | 0d7a81a08e35c6afb03088da66fd6bb164f62f5f3ed1d964e0bbf05669487a22 | lean_source_file | pkg_mathlib_source_file_chunks | induction n with
| zero => simpa using base
| succ n ih =>
exact fun x hx => (Ico_subset_Ico_union_Ico hx).elim (ih x) (step (n + 1) (by simp) ih _)
end Induction |
6,918 | lean_file_chunk | 2f76103c0652588d6156663cc92f8772abe2bc75bc48c2b932639462e6aedf56 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
public import Mathlib.Data.EReal.Basic
/-!
# Ext... |
23,722 | lean_file_chunk | 779a045817b9e1aa2fe66f23242faefc91360571e227302c76c1b95885034bd4 | 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, Jean Lo, Calle Sönne
-/
module
public import Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Nat.Factorization.Defs
public impor... |
6,323 | lean_file_chunk | 2648eb20e474e2e08d3b7bf83a23b98f2183e6fb44a4e311ce2ac314a28d54dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine, Pietro Monticone, Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.ERealExp
public import Mathlib.Analysis.SpecialFunctions.L... |
7,274 | lean_file_chunk | 38a9230470dbebb11e75bf45a9ea92bb44189c8a2f215c34c10b6acd85ea7c7f | 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.Log.Basic
/-!
# The Positive Part of the Logarithm
This file defines the function `Real.posLog = r ↦ max 0 (... |
2,713 | lean_file_chunk | b1e5548e6ca675c4cb080ad8bfeecf5b82eaee383e39995933e295653c01712f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Bolton Bailey. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bolton Bailey
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Logarithm Tonality
In this file we describe the tonality of the logarithm function when multipl... |
3,855 | lean_file_chunk | ef57d614359a9c04b9fa953b4105f8d548c27904bb29be7a16344565ba47e11b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SpecialFunctions.Pow.Real
/-!
# The logarithm as a limit of powers
This file shows that the logarithm can be expressed as a... |
8,238 | lean_file_chunk | 6e9024de03237b7e6dc308b0fb61f98d2a7f188c49e17f3bfa6f07eee2222bce | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Deriv
public import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
public import Mathlib.Analysis.Convex.De... |
14,393 | lean_file_chunk | 580cfbefd9f75d6c58a590b18b5ca7bb071db16d7ec9f6cfb9d32fadbe4fc829 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yuval Filmus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuval Filmus
-/
module
public import Mathlib.RingTheory.Polynomial.Chebyshev
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
public import Mathlib.Analysis.SpecialFu... |
6,000 | lean_file_chunk | d35823e8acf8d8ce52d9ccc87fbd88b3780e9a286883090fc5ff715ffe98fc0c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yuval Filmus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuval Filmus
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonali... |
6,259 | lean_file_chunk | ba4b1a5325ddd2de43f653a112e9b336416a4929da1a4ba78e5ecfd60fda8f4b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yuval Filmus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuval Filmus
-/
module
public import Mathlib.RingTheory.Polynomial.Chebyshev
public import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
import Mathlib.Analysis.SpecialFunctions... |
7,398 | lean_file_chunk | a60c15512a776f732b75c3c165c211f67715d92f22e547e7b8350f83b1851194 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Complex.Trigonometric
public import Mathlib.LinearAlgebra.Complex.Module
public import Mathlib.RingTheory.Polynomial.Chebyshev
... |
14,526 | lean_file_chunk | 99d96340304cb954108c503830dc9e04604bf44a6d7c86ff84dd08a5316c18dd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yuval Filmus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yuval Filmus
-/
module
public import Mathlib.RingTheory.Polynomial.Chebyshev
public import Mathlib.Data.Real.Basic
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
pu... |
3,783 | lean_file_chunk | e390eea9ce39e66a4e04bc686ca64dbc069ca4e98bc4d3b0cb1a9fc80a879608 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.CStarAlgebra.ContinuousFunctionalCalculus.Basic
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.... |
7,207 | lean_file_chunk | 4426aadffdd6d395661f46b2dc6e2ed1a4fe740756ec6d35a4461079a5fd2a4b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.SpecialFunctions.Exponential
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique
public import Ma... |
2,070 | lean_file_chunk | e51c19d54d2669d08e189e7bfc103c0269c86122145958bfc321d84c4ca8871f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalcu... |
14,119 | lean_file_chunk | 30041e6d536907bca56a5aec7441c73c5753950e35656a2dacb9c3a84c734a67 | 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.Unique
public import Mathlib.Topology.ContinuousMap.ContinuousSqrt
public import Mathli... |
4,451 | lean_file_chunk | 201c6f70dd91ded46b0356ee2fe3b8585e8f46b4817c4e46a026c5ff50cf5794 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalc... |
3,985 | lean_file_chunk | 8d55d5eb09406efaa168301b76191e7f25d102ee596b1b798e24e36aad49f7c8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.CStarAlgebra.ContinuousFunctionalCalculus.Basic
public import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.... |
23,974 | lean_file_chunk | 290650a23f648e4ccf6ff20a761c7631e737c3a8a5d97103e026e72a80b23975 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Algebra.Order.Star.Prod
public import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances
public import Mathlib.Analy... |
10,744 | lean_file_chunk | 24b666f4a50bc6e9685e24849149e890da59c5d93e4f5944fb544bb8f5c9a0e2 | lean_source_file | pkg_mathlib_source_file_chunks | [ContinuousFunctionalCalculus ℝ (∀ i, C i) IsSelfAdjoint]
[∀ i, IsSemitopologicalRing (C i)] [∀ i, T2Space (C i)]
[NonnegSpectrumClass ℝ (∀ i, C i)] [∀ i, NonnegSpectrumClass ℝ (C i)]
set_option backward.isDefEq.respectTransparency false in
/- Note that there is a higher-priority instance of `Pow (∀ i, B i) ℝ` com... |
23,955 | lean_file_chunk | dbfa41309b63294360372b32fbd6573affb3fbb2f1fb937f85e3652ee2d6dffb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.CStarAlgebra.ContinuousFunctionalCalculus.Integral
public import Mathlib.Analysis.CStarAlgebra.ApproximateUnit
import Mathlib... |
3,207 | lean_file_chunk | 50a7d29e9e6b8698b4354bcaf147a3648b51da774fd479fb8cba4577b137b37c | lean_source_file | pkg_mathlib_source_file_chunks | obtain ⟨μ, hμ⟩ := exists_measure_rpow_eq_integral_rpowIntegrand₁₂ hp
refine ⟨μ, fun a (ha : 0 ≤ a) => ?_⟩
have hpcoe : (p : ℝ) ∈ Ioo 1 2 := by exact_mod_cast hp
let f t := rpowIntegrand₁₂ p t
let maxr := sSup (quasispectrum ℝ a)
have maxr_nonneg : 0 ≤ maxr :=
le_csSup_of_le (b := 0) (IsCompact.bddAbove (q... |
3,294 | lean_file_chunk | 015dacda46e941c7a5f6ab01c63e2b5e34dd7bfb3f2f8a7155d078ae4393ec75 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
/-!
# Conjugating by the square root of a positive element in a C⋆-... |
3,870 | lean_file_chunk | 9e7308715f4c46718e942817b322a74796393bd905f49be61a8e4a3936de27cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
import Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculu... |
18,125 | lean_file_chunk | 523f7ee73d296d1751a3571a1849c33e58cac511f3b77cada0c2e283bb296b70 | 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.Data.NNReal.Basic
public import Mathlib.Order.Fin.Tuple
public import Mathlib.Order.Interval.Set.Monotone
public import Mathlib.Topolo... |
7,604 | lean_file_chunk | 88854624a54a0106c831aee344f832aaf6e408ca8c9c109d7a98eda869480f83 | 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.BoxIntegral.Box.Basic
public import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Induction on subboxes
In this file we prove... |
15,638 | lean_file_chunk | 0f19cf1706239d6e06dbefcabbdb571e56d5b1d92552d4ea7974ab28b23abf59 | 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.BoxIntegral.Partition.Basic
/-!
# Tagged partitions
A tagged (pre)partition is a (pre)partition `π` enriched with a tagged ... |
9,188 | lean_file_chunk | 5db4f995609eeeca907fb56be2303742031f3a56532af6fde161cda1c4a5f3cb | 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.BoxIntegral.Partition.Split
public import Mathlib.Analysis.Normed.Operator.Mul
/-!
# Box additive functions
We say that a f... |
15,284 | lean_file_chunk | 20c2272c560855f72c5e152ff4217449144cd39ca50edceb0aba8d820a5b4410 | 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.BoxIntegral.Partition.Basic
/-!
# Split a box along one or more hyperplanes
## Main definitions
A hyperplane `{x : ι → ℝ |... |
23,993 | lean_file_chunk | 69e2b42dde016b5127aab497a9a9d996d6a9fd4d6b1b03f3f4cbae0592d30993 | 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.Algebra.BigOperators.Option
public import Mathlib.Analysis.BoxIntegral.Box.Basic
public import Mathlib.Data.Set.Pairwise.Lattice
/-!
... |
3,676 | lean_file_chunk | dd7bd0c84910e40a88072155192105c71dfe0ab9725597ca01229d492a65f6d9 | lean_source_file | pkg_mathlib_source_file_chunks | def distortion : ℝ≥0 :=
π.boxes.sup Box.distortion
theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
le_sup h
theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π, Box.distortion J ≤ c :=
Finset.sup_le_iff
theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartiti... |
23,992 | lean_file_chunk | 83b68d1cb7921bc1536cfe7d460afaeb58f5693547fd15a4904da22e481e7c71 | 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.BoxIntegral.Partition.SubboxInduction
public import Mathlib.Analysis.BoxIntegral.Partition.Split
/-!
# Filters used in box-b... |
2,895 | lean_file_chunk | f945208d85980af753e3defa62f8fe57f060fed81e47d90045d06a83934180e2 | lean_source_file | pkg_mathlib_source_file_chunks | (l.hasBasis_toFilterDistortioniUnion J _ _)).2 fun r hr => ?_
refine ⟨r, hr, fun π hπ => ?_⟩
rw [mem_setOf_eq, Prepartition.iUnion_top] at hπ
refine ⟨⟨hπ.1.1, hπ.1.2, fun hD => le_trans (hπ.1.3 hD) (le_max_left _ _), fun _ => ?_⟩, ?_⟩
· refine ⟨_, π₀.iUnion_compl.trans ?_, le_max_right _ _⟩
congr 1
exac... |
9,989 | lean_file_chunk | 36690534020e5d4d439f6aef89736c995ccdcc18660cb793853a454e397ce953 | 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.BoxIntegral.Box.SubboxInduction
public import Mathlib.Analysis.BoxIntegral.Partition.Tagged
/-!
# Induction on subboxes
In ... |
4,405 | lean_file_chunk | f493328558e16a15ed3ba5d7632218fdf3231375ca31c039dea22e8241b2ca35 | 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.BoxIntegral.Partition.Additive
public import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
/-!
# Box-additive functions defin... |
237 | lean_file_chunk | 5d61e1a309282893dab9921e16431083afe8109f373a07a7421d96914c66d597 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Data.EReal.Inv
public import Mathlib.Data.Real.Sqrt
deprecated_module (since := "2025-11-21") |
467 | lean_file_chunk | 1c05c2d5a1ee43d26aa1fce82864d27ef4750bfd719d225850a23b56bab15955 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Algebra.Order.BigOperators.Expect
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Data.EReal.Inv
public import Mathlib.Data.Nat.Totient
public import Mathlib.Data.Real.Sqrt
public import Mathlib.Data.Sym... |
555 | lean_file_chunk | 4581a3abd5471cb286ec0423ab36d565202ca7ef9a4087225d30d7f9cd6ee175 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Algebra.Order.BigOperators.Expect
public import Mathlib.Algebra.Order.Field.Power
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Data.EReal.Inv
public import Mathlib.Data.Nat.Totient
public import Mathl... |
314 | lean_file_chunk | 2c08bb8213b816fcdda86ff98c476946dc82fe77d8afc3d3f519ec3a0a8604ce | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Analysis.Normed.Group.Basic
public import Mathlib.Data.EReal.Inv
public import Mathlib.Data.Real.Sqrt
public import Mathlib.Data.Sym.Sym2
public import Mathlib.Tactic.NormNum.GCD
deprecated_module (since := "2025-11-21") |
14,460 | lean_file_chunk | f3ecc9da08b66c23671c4680c7f9f88ec5492c67cfff5a727ad295634485cd2d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Ziyu Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ziyu Wang, Chenyi Li, Sébastien Gouëzel, Penghao Yu, Zhipeng Cao
-/
module
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Mathlib.Analysis.Calculus.FDeriv.Basic
public... |
953 | lean_file_chunk | 97a3d4d1c046e74f697731cd8c991fa10e504b896f901a82250e5bdecb3f5fd7 | 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.Calculus.ContDiff.Operations
public import Mathlib.Topology.Algebra.ContinuousAffineMap
public import Mathlib.Analysis.Normed.Group.A... |
707 | lean_file_chunk | cc9e74c6dac0b9ca48a9cc08b5e0dc6194bdec672543923f169a57e42ea64b9a | 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.Calculus.AddTorsor.AffineMap
public import Mathlib.Analysis.Normed.Affine.AddTorsorBases
/-!
# Barycentric coordinates are smooth
-/... |
10,352 | lean_file_chunk | 9029d53390844a820d49fc5686f457517be5eb3698412272e7345c545fd11015 | 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.Calculus.FDeriv.Mul
public import Mathlib.Analysis.Calculus.FDeriv.Comp
/-!
# Fréchet Derivative of `f x ^ n`, `n : ℕ`
In this file... |
23,993 | lean_file_chunk | d351955e020e9132c261993be1d4f69084b006fd288f5ea626f2cd9d0cd32c91 | 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.CPolynomial
public import Mathlib.Analysis.Analytic.Inverse
public import Mathlib.Analysis.Analytic.Within
public im... |
20,588 | lean_file_chunk | 29763d0ecac03f6ffc342e663ba08c7404571f37d26739a8abc03a0c6a3a6adf | lean_source_file | pkg_mathlib_source_file_chunks | fun _ hy ↦ (h.cpolynomialAt_of_mem hy).analyticAt.differentiableWithinAt
theorem HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt (h : HasFiniteFPowerSeriesOnBall f p x n r)
{y : E} (hy : (‖y‖₊ : ℝ≥0∞) < r) :
HasStrictFDerivAt f (continuousMultilinearCurryFin1 𝕜 E F (p.changeOrigin y 1)) (x + y) :=
(h.changeOr... |
4,470 | lean_file_chunk | 475446c1463b7be71b0cd74e392e1e63379ecc47e5a809d4e20b86977bb1b2a4 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Basic
/-!
# The derivative of the scalar restriction of a linear map
For de... |
6,099 | lean_file_chunk | 5e67c765aad28feb911f8c75f3ad415d1c0834be14ab86856fde4c24705be4b5 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Prod
/-!
# The derivative of bounded bilinear maps
For detailed documentati... |
13,041 | lean_file_chunk | 4235741725fd3d65e1a7a35783820f13a20d2d942c790e06cb08c6281e5507b0 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Basic
/-!
# The derivative of a composition (chain rule)
For detailed docum... |
23,974 | lean_file_chunk | e912365d7bb5dd2274abd107d574642f1ed9df5684e4498a2b4a0e5d3f4ff715 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Linear
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Math... |
12,041 | lean_file_chunk | 7edfb2f9801918f032d456b3a3beebc5819d3ee0e1d9fc26892573977fd763d2 | lean_source_file | pkg_mathlib_source_file_chunks | @[to_fun (attr := simp)]
lemma DifferentiableAt.add_iff_right (hg : DifferentiableAt 𝕜 f x) :
DifferentiableAt 𝕜 (f + g) x ↔ DifferentiableAt 𝕜 g x := by
simp only [add_comm f, hg.add_iff_left]
@[to_fun (attr := simp)]
lemma DifferentiableAt.sub_iff_left (hg : DifferentiableAt 𝕜 g x) :
DifferentiableAt �... |
5,027 | lean_file_chunk | b0ddd60078efbc2e7a0b07cb56cd9a2b10c8bfcaf3499a60427e581982eff006 | 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.Analysis.Calculus.FDeriv.Linear
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus.FDeriv.Equiv
publi... |
8,724 | lean_file_chunk | 24753857f4659e6bfa4a204d44eacf4927eea907d396fc2a587f22f18b90ccdd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Calculus.Deriv.Abs
public import Mathlib.Analysis.Calculus.LineDeriv.Basic
/-!
# Differentiability of the norm in a real norme... |
23,985 | lean_file_chunk | 618d43c008e11f2fe967444885b6614334d95531ecd7ed202f0805260b37f3e0 | 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, Sébastien Gouëzel, Yury Kudryashov, Eric Wieser
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus.FDeriv.Const
public... |
1,842 | lean_file_chunk | 8c4f19303461ce97592dbe9707c8cf5205cbccf1702cfefdc23b8627bd4753e1 | lean_source_file | pkg_mathlib_source_file_chunks | differentiableAt_finCons
@[fun_prop]
theorem DifferentiableAt.finCons
(h : DifferentiableAt 𝕜 φ x) (hs : DifferentiableAt 𝕜 φs x) :
DifferentiableAt 𝕜 (fun x => Fin.cons (φ x) (φs x)) x :=
differentiableAt_finCons'.mpr ⟨h, hs⟩
theorem differentiableOn_finCons :
DifferentiableOn 𝕜 (fun x => Fin.cons ... |
11,127 | lean_file_chunk | 3d678f21ac00b752aa8cab890a3ea475e0da1f9173f87eaa90ff925d11d6d92b | 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.Calculus.FDeriv.ContinuousMultilinearMap
public import Mathlib.Analysis.Normed.Module.Alternating.Basic
/-!
# Derivatives of... |
4,355 | lean_file_chunk | 7798e324442a54a2a65a99209867943e87b9529e703e0b8680849160d187f99c | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Basic
public import Mathlib.Analysis.Normed.Operator.BoundedLinearMaps
/-!
#... |
6,765 | lean_file_chunk | a05fb189c133ac20cfce70be652730560c75ea17557697f7e48cf6dd7c22bb6e | 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.Calculus.FDeriv.Analytic
public import Mathlib.Analysis.Calculus.FDeriv.CompCLM
/-!
# Derivatives of operations on continuou... |
1,240 | lean_file_chunk | 846199ea57eac06e1b867ca5db6319928b13cdcf1767fb7c5f320d030a97648a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Prod
public import Mathlib.Analysis.Calculus.FDeriv.Const
/-!
# Derivatives on pi-types.
... |
23,920 | lean_file_chunk | 6da57546ba777defc11a68d184b1ee66808c71554c99289e93bc88e62806332e | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Analytic.Constructions
public import Mathlib.Analysis.Calculus.FDeriv.Analytic
public import ... |
10,063 | lean_file_chunk | 358fc0188e3c7111d74d63d25f2ef6154df5a9ba4448a221d83348c1ea43739c | lean_source_file | pkg_mathlib_source_file_chunks | (fderivWithin 𝕜 (fun x ↦ f l[i] x) s x) <• ((l.drop (.succ i)).map (f · x)).prod :=
(HasFDerivWithinAt.list_prod' fun i hi ↦ (h i hi).hasFDerivWithinAt).fderivWithin hxs
@[fun_prop]
theorem HasStrictFDerivAt.multiset_prod [DecidableEq ι] {u : Multiset ι} {x : E}
(h : ∀ i ∈ u, HasStrictFDerivAt (g i ·) (g' i) x)... |
23,977 | lean_file_chunk | 81e06286b7595dde7d065e7aa0ec4b15e5ad80b518ca9547ffb2cbfe36cfdb1d | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Asymptotics.Defs
public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
public impor... |
18,733 | lean_file_chunk | 8d7ae3ffb1e690907ca781f2151ad3905e45323bb69d47acac2680790eacae50 | lean_source_file | pkg_mathlib_source_file_chunks | · exact (hf x hx).differentiableAt (hs.mem_nhds hx) |>.differentiableWithinAt
· exact (hf' x hx).differentiableAt (ht.mem_nhds hx) |>.differentiableWithinAt
/-- A function is differentiable on two open sets iff it is differentiable on their union. -/
lemma differentiableOn_union_iff_of_isOpen (hs : IsOpen s) (ht : I... |
12,031 | lean_file_chunk | aecc4c1e430ed97972a8f659861de8ae60f4baafa38cb39b19fdb1936fd721a4 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Basic
/-!
# The Fréchet derivative: congruence properties
Lemmas about cong... |
10,132 | lean_file_chunk | 34e213ba84b98bf8f22bd48c1191df25114ebf5ff07e5acde4651d36a5d31f4f | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Asymptotics.TVS
/-!
# The Fréchet derivative: definition
Let `E` and `F` be normed spaces, ... |
14,088 | lean_file_chunk | 923c05b4ad074696724a18ae1adf4dc993ad7cec978a553a5220fa9984571471 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Congr
/-!
# Fréchet derivative of constant functions
This file contains the... |
23,997 | lean_file_chunk | fecd9e7468b5a8b1ca4648d27fcbaea4c8ef3ded40c5e0a1d49a98075b1dfdf6 | 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, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Basic
public import Mathlib.Analysis.Calculus.Deriv.Slope
public import Mathlib.Analysis.... |
23,980 | lean_file_chunk | 2aa24838667db28b7a04efece24b064d1a24124eb59561de2ccbfd0c812baddd | lean_source_file | pkg_mathlib_source_file_chunks | ‖f z - f y - (z - y) • L‖ ≤ ε * r := by
rcases hx with ⟨r', r'mem, hr'⟩
have A : x + r / 2 ≤ x + r' := by linarith [r'mem.1]
exact hr' _ ((Icc_subset_Icc le_rfl A) hy) _ ((Icc_subset_Icc le_rfl A) hz)
theorem mem_A_of_differentiable {ε : ℝ} (hε : 0 < ε) {x : ℝ}
(hx : DifferentiableWithinAt ℝ f (Ici x) x) :
... |
279 | lean_file_chunk | a463beb8fa15f55632f28ffae185796ef48a076124314b045681a94561e7891a | lean_source_file | pkg_mathlib_source_file_chunks | [OpensMeasurableSpace 𝕜] [SecondCountableTopologyEither α F]
{f : α → 𝕜 → F} (hf : Continuous f.uncurry) (μ : Measure (α × 𝕜)) :
AEStronglyMeasurable (fun (p : α × 𝕜) ↦ deriv (f p.1) p.2) μ :=
(stronglyMeasurable_deriv_with_param hf).aestronglyMeasurable
end WithParam |
13,783 | lean_file_chunk | 9b3a767d94fcca150cd2bbea2c77e12c78848f2a8cbda4c4ecc6f48fe43888a6 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import Mathlib.Analysis.Normed.Module.Alternating.Basic
/-!
... |
23,965 | lean_file_chunk | f480e2e5236a32d637483a888b0521d09ced94c7d51cd64d4ac9a4a81593a0e5 | 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, Sébastien Gouëzel, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
public import Mathlib.Analysis.Calculus.FDeriv.Add
public im... |
4,097 | lean_file_chunk | 918a64b2cde8fa30c6222cb0eeb7c2a82af9678641715debab3b0f36e309c25a | lean_source_file | pkg_mathlib_source_file_chunks | exact h.mapsTo_tangent_cone.mono Subset.rfl Submodule.subset_span
theorem UniqueDiffOn.image {f' : E → E →L[𝕜] F} (hs : UniqueDiffOn 𝕜 s)
(hf' : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x) (hd : ∀ x ∈ s, DenseRange (f' x)) :
UniqueDiffOn 𝕜 (f '' s) :=
forall_mem_image.2 fun x hx => (hf' x hx).uniqueDiffWithi... |
3,624 | lean_file_chunk | 02c08ea3e147c4c0aad67262f513da9db587d0821473328e0a71b1a93b462c1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Eric Wieser
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Prod
public import Mathlib.Analysis.Calculus.FDeriv.Equiv
public import Mathlib.Analysis.Norme... |
23,931 | lean_file_chunk | edaf5ff8d9b320178553fa8c665daa4d14b994103258a543c1e1ec05cd77c772 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Analytic.IteratedFDeriv
public import Mathlib.Analysis.Calculus.Deriv.Pow
public import Mathlib.Analysis.Calculus.MeanVal... |
8,098 | lean_file_chunk | e688fd0fa0f790f59f3696ded460e04efbd1e953c2018f4885a4c33523843897 | lean_source_file | pkg_mathlib_source_file_chunks | (fun y hy => hε (interior_subset hy)) (Metric.mem_ball_self εpos) hx.hasFDerivWithinAt v w
end Real
section IsRCLikeNormedField
variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
{E F : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
[NormedSpace 𝕜 F] {s : Set E} {f : E → F} {x : E}
the... |
2,236 | lean_file_chunk | 53012a27c39e1ceb7d3105142ce8e8b421f4f0cc36155ac31434e4e670319b41 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Calculus.FDeriv.Add
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.Topology.Algebra.Continuo... |
11,215 | lean_file_chunk | 10969493b7901e70e49fb6ffba373520a8bfabc71fee9eb13eee372eede4e29f | 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.Calculus.MeanValue
/-!
# Extending differentiability to the boundary
We investigate how differentiable functions inside... |
12,829 | lean_file_chunk | 888dfc63522c800791d92223f802ab6a6b3abe9dabd144660d45d180de351602 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov, Sam Lindauer
-/
module
public import Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin
public import Mathlib.Analysis.Calculus.FDeriv.Symmetric
public imp... |
8,788 | lean_file_chunk | e30ebd5963ab724e4784b328a72207ea28dc1b9263649f289f0f6a1e571f3b83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
module
public import Mathlib.Analysis.Calculus.DifferentialForm.Basic
public import Mathlib.Analysis.Calculus.FDeriv.ContinuousAlternatingMap
public import M... |
22,504 | lean_file_chunk | 062de2930ac972a542a8bcae9ae64dfeecec3488c5ba28f40de83f900506cc0e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, Ruben Van de Velde
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Deriv
public import Mathlib.Analysis.Calculus.ContDiff.Operations
public import Mathlib.A... |
12,867 | lean_file_chunk | afb44069edd6af2577807694bd1b0fc838b6def24978ccb50d327f88cf4d3531 | 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.Calculus.ContDiff.Comp
public import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
/-!
# Iterated derivatives of compositions... |
19,452 | lean_file_chunk | 5f769ed7feaff31c45a6e5ccc78e5a3b0bd40f230fc93b2098d9041e56d97661 | 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
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Deriv
/-!
# One-dimensional iterated derivatives
We define the `n`-th derivative of a function `f : �... |
1,123 | lean_file_chunk | a8cdae736d7e27e21836563cd580622843369ac85c8752a0446874964898cb6a | 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.Calculus.IteratedDeriv.Defs
public import Mathlib.Analysis.Calculus.Deriv.ZPow
/-!
# Derivatives of `x ^ m`, `m : ℤ` within an... |
2,717 | lean_file_chunk | f4f0d1b5e164497921cde61b92a8f0446fbaf10657366bd72ee082a9d02d9558 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Vasilii Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasilii Nesterov
-/
module
public import Mathlib.Analysis.Analytic.Uniqueness
public import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
public import Mathlib.Analysis.Normed.Module... |
23,943 | lean_file_chunk | 9d9914f88f247b6090a7e11898965531d9b0060b836a600a330f81816e9848d5 | 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.Calculus.FDeriv.Add
public import Mathlib.Analysis.Calculus.FDeriv.Equiv
public import Mathlib.Analysis.Calculus.FormalMu... |
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