Datasets:
formalmathatepfl
/
lean-docs

Dataset card Data Studio Files
xet
 Community
1
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
1,138
lean_file_chunk
43ef2336615a33c1d1955187a625b7130b261b7f20df97138b17d76b09c8d8f7
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 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.Convex.Basic public import Mathlib.Algebra.Order.Module.Field public import Mathlib.Data.NNReal.Defs /-! # Specific lemmas...
13,945
lean_file_chunk
5b787e30a6e26e4a83737b8679a895992274d4d815c0d0168d7e717802e6cdfd
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 Paul Reichert. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Reichert, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Normed.Affine.AddTorsorBases /-! # Intrinsic frontier and interior This file defines the intrinsic frontier, inte...
3,526
lean_file_chunk
31d0e3183224943f5bf9e164c3a730857ec9048e7b8689381194c9a0a77f02f8
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.Topology.PartitionOfUnity public import Mathlib.Analysis.Convex.Combination /-! # Partition of unity and convex sets In this file we...
15,277
lean_file_chunk
babd8c81205fb2e58e56f9246707eb744b675b6a1185b69bad7b21f9d7d0313c
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2019 Alexander Bentkamp. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alexander Bentkamp, Yury Kudryashov, YaΓ«l Dillies, JoΓ«l Riou -/ module public import Mathlib.Analysis.Convex.Combination public import Mathlib.Analysis.Convex.PathConnected public...
6,645
lean_file_chunk
f1be740cbb0290922b2436c53b60a6b795afb9e228ca798e43bae720fcffe834
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta -/ module public import Mathlib.LinearAlgebra.Matrix.Stochastic /-! # Doubly stochastic matrices ## Main definitions * `doublyStochastic`: a square matrix is doubly stoc...
6,273
lean_file_chunk
63ff47fa7a46f3e417773f596c2dcde64a04cdc143c352f67758dea1cabd7231
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ module public import Mathlib.Analysis.Convex.Exposed public import Mathlib.Analysis.LocallyConvex.Separation public import Mathlib.Topology.Algebra.ContinuousAffineMap ...
14,708
lean_file_chunk
dfae80b64ef4513e088dc794b9a385c24d2cdec5f2da27ed2b035a3241475c0a
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2021 YaΓ«l Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: YaΓ«l Dillies -/ module public import Mathlib.Analysis.Convex.Basic public import Mathlib.Topology.Algebra.Group.Pointwise public import Mathlib.Topology.Order.Basic /-! # Strictly conv...
2,789
lean_file_chunk
ae09acd7b8be6c70698cee910f8f3bed92c71692ca6774b2d909f6672b2f9579
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Convex.ContinuousLinearEquiv public import Mathlib.Analysis.Convex.StrictConvexSpace public import Mathlib.Analysis.Normed.Op...
20,157
lean_file_chunk
61ef175d40acf0e771c81f1a2b84d71817463af7f87984b2cfea794a03d2979d
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 Adomas Baliuka. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Adomas Baliuka -/ module public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog public import Mathlib.Analysis.Convex.SpecificFunctions.Basic /-! # Properties of Shannon q-ary...
5,222
lean_file_chunk
2d8ab1bd1c9f9b3e9753285d4cfbf2b5d4a3c23566a425c7d09f9142a994c333
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Horner -/ module public import Mathlib.Algebra.BigOperators.Field public import Mathlib.Analysis.Convex.Deriv public import Mathlib.Analysis.Convex.Piecewise public import M...
19,882
lean_file_chunk
e479c451c7a6045cffbacd60a3cfdde2e768125cd9d9a1785458edad5c5ccedf
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 SΓΆnne -/ module public import Mathlib.Analysis.Complex.Asymptotics public import Mathlib.Analysis.Complex.Trigonometric public imp...
9,485
lean_file_chunk
488cd71fa89047862eb09a173c7ac898c60cd143a416f75c80a36bf173850755
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 Edward Watine. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Edward Watine -/ module public import Mathlib.Analysis.Analytic.OfScalars public import Mathlib.Analysis.RCLike.Basic /-! # Ordinary hypergeometric function in a Banach algebra In th...
6,110
lean_file_chunk
945f576e10d2ce787aebc4aa57e0656000c5b2ce30c03aa5899a2b43fe4a55ee
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.Calculus.ContDiff.Operations public import Mathlib.Analysis.Calculus.Deriv.Pow /-! # Smoothness of `Real.sqrt` In this file...
5,758
lean_file_chunk
26bb07d3ec2ff05496a396489d1fd53f806beb25a58b41164d889d6b078a7c8c
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.Analysis.SpecialFunctions.Log.Basic /-! # Inverse of the tanh function In this file we define an inverse of tanh as a function from ℝ to (...
905
lean_file_chunk
20106964d9c2093132cfcef7619231cef383c2dd443b54e1bcfa7b82c9826d26
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.SpecialFunctions.Exp /-! # Limits of `P(x) / e ^ x` for a polynomial `P` In this file we prove that $\lim_{x\to\infty}\frac...
11,531
lean_file_chunk
6285840886eda12ed1e9865bce0fb90d4078cb559048ea096f37b92a61ead8ba
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 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.SpecificLimits.Basic public import Mathlib.Data.Real.Sqrt /-! # The arithmetic-geometric mean Starting with two nonnegative real numb...
13,712
lean_file_chunk
6425d0ba8da24dfe44400e531705a8cf0ffa173e20accf892c2b4d23d4fe2dba
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.Analysis.SpecialFunctions.MulExpNegMulSq public import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds public import Mathlib.MeasureTh...
7,615
lean_file_chunk
f8b4df034d0a1858e3bb2ce9ced9700e49ba2d4a1945f0a155f7e43fa0366ac1
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.Analysis.SpecialFunctions.Log.Basic public import Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp /-! # Inverse of the cosh functi...
18,915
lean_file_chunk
570fcf6e946d692cfc9b75f5b082e2d4a49d069945af7c483d62205c5fa33eb4
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ module public import Mathlib.Analysis.Normed.Algebra.Exponential public import Mathlib.Analysis.Calculus.FDeriv.Analytic public import Mathlib.Analy...
12,223
lean_file_chunk
0a2836901ffdcda18140b1fd6ca943b700093847f082068b68726f5506fa844d
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.SpecialFunctions.Log.Deriv public import Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus /-! # Non-integrabl...
11,916
lean_file_chunk
cfb983f6eedb85055203fdf3264d7913992d30f4142716085a3443f837dea8c4
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.Algebra.BigOperators.Field public import Mathlib.Analysis.Convex.Gauge public import Mathlib.Analysis.Normed.Order.Lattice public import Mat...
7,116
lean_file_chunk
818d89c1a6ed8b32ae7e6e7803c7957f7c21063b0fcbd72477de90ec840111df
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 Jakob Stiefel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jakob Stiefel -/ module public import Mathlib.Analysis.SpecialFunctions.ExpDeriv public import Mathlib.Analysis.SpecialFunctions.Log.Basic public import Mathlib.Topology.ContinuousMap....
10,317
lean_file_chunk
988715fb5b5b4dd3ca0fd9b03f71fdcaf156e058ad2d3b1d0acf6fe88de29b08
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 GaΓ«tan SerrΓ©. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: GaΓ«tan SerrΓ©, RΓ©my Degenne -/ module public import Mathlib.Analysis.Calculus.Deriv.Inv public import Mathlib.Analysis.InnerProductSpace.Basic public import Mathlib.Analysis.SpecialFunct...
6,525
lean_file_chunk
3ff1330955291d8ee2a8395f19317376291579dd225b3b462e9fbc4350b3594d
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.SpecialFunctions.Integrability.Basic public import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar public import Mathlib.MeasureTheory....
13,985
lean_file_chunk
817ca42fa597f6f6f4be781c7c1ee5af16780b8b78f35a5424f7023c76ccba40
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.MeasureTheory.Function.Jacobian public import Mathlib.MeasureTheory.Measure.Lebesgue.Complex public import Mathlib.Analysis.Specia...
9,630
lean_file_chunk
7c033afc29606d367db80f2a888acd60a218aad798066b02f9ad664f8b8bbdc9
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.SpecialFunctions.Pow.Asymptotics public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent public import Mathlib.Analys...
13,589
lean_file_chunk
b8ee731c33a43b8400241fdedb2f6541597450f0f6e90f9e4fe68ce17215a46b
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 SΓΆnne -/ module public import Mathlib.Analysis.Calculus.ContDiff.RCLike public import Mathlib.Analysis.Calculus.IteratedDeriv.Lemm...
9,490
lean_file_chunk
2248a442df6067e7993380debd125a695cbfbeb8288c3c323b82235a35843e9b
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.Deriv.Inv public import Mathlib.Analysis.Calculus.Deriv.Polynomial public import Mathlib.Analys...
9,381
lean_file_chunk
0349e024f7549fc6f0a3bad0ff97f470f0f50a217a464428884bc48f196f2f0e
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2020 James Arthur. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: James Arthur, Chris Hughes, Shing Tak Lam -/ module public import Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp public import Mathlib.Analysis.SpecialFunctions.Log.Basic /-!...
14,417
lean_file_chunk
ee65f8345b00346e5880faa6777dbe8a84ab9b31e93fafe3fd38f0e7a058ce4f
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 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.SpecialFunctions.JapaneseBracket public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic public import Mathlib.MeasureT...
13,064
lean_file_chunk
df0a545360b36e7ec5a0a5c12de4f2aab9b8084cda58bd68bd2879c377f698c5
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 Moritz Firsching. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Firsching, Fabian Kruse, Nikolas Kuhn -/ module public import Mathlib.Analysis.PSeries public import Mathlib.Analysis.Real.Pi.Wallis public import Mathlib.Tactic.AdaptationNo...
2,167
lean_file_chunk
c9524e6ba70cf40678a6f7056dde17a364154165f3e9914957a86328fbbe6466
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Mitchell Horner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Horner -/ module public import Mathlib.Analysis.SpecificLimits.Basic public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent public import Mathlib.Data.Nat.Cast.Fiel...
1,252
lean_file_chunk
8b7a2c06a636e0e1ed522a90392870695b0afed8654d6e63633ff52592d733fb
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 Xavier GΓ©nΓ©reux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier GΓ©nΓ©reux, Patrick Massot -/ module public import Mathlib.Analysis.SpecificLimits.Basic public import Mathlib.Analysis.RCLike.Basic /-! # A collection of specific limit comput...
23,925
lean_file_chunk
67b349e48f5c7626a0176aae6474793578caf7a8b4a4dd43719fdad84472411c
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, SΓ©bastien GouΓ«zel, Yury Kudryashov, Dylan MacKenzie, Patrick Massot -/ module public import Mathlib.Algebra.BigOperators.Module public import Mathlib.Algebra.Orde...
22,675
lean_file_chunk
b9b723d072d45c36c9820b4dae7c853bef427d2ec80e18135830e18fa7e11451
lean_source_file
pkg_mathlib_source_file_chunks
simp only [P, natDegree_comp, ascPochhammer_natDegree, mul_one, natDegree_X_add_C] have A : (n + k).descFactorial k = P.eval n := by have : n + 1 + k - 1 = n + k := by lia simp [P, ascPochhammer_nat_eq_descFactorial, this] conv_lhs => rw [A, mP.as_sum, dP] simp [eval_finset_sum] have : Summabl...
1,435
lean_file_chunk
9a181bcd50d7dfd8b37f5d16657b341eabc3ea76f1160d69edc17f7b8bac5b67
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Snir Broshi. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Snir Broshi -/ module public import Mathlib.Analysis.SpecificLimits.Normed public import Mathlib.NumberTheory.Real.GoldenRatio /-! # The ratio of consecutive Fibonacci numbers We prove...
23,951
lean_file_chunk
3920be5a900c77b034add20dba6944a3740d66c2b7c74ff789d7204673b30fec
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Johannes HΓΆlzl, Yury Kudryashov, Patrick Massot -/ module public import Mathlib.Algebra.Field.GeomSum public import Mathlib.Data.Nat.Factorial.BigOperators public i...
11,920
lean_file_chunk
2c6a0073a7e8e22cfcf4ca4a1f9458acfd4f15a036ef13de61f6e07b40b3f67a
lean_source_file
pkg_mathlib_source_file_chunks
variable [PseudoMetricSpace Ξ±] {r C : ℝ} {f : β„• β†’ Ξ±} section variable (hr : r < 1) (hu : βˆ€ n, dist (f n) (f (n + 1)) ≀ C * r ^ n) include hr hu /-- If `dist (f n) (f (n+1))` is bounded by `C * r^n`, `r < 1`, then `f` is a Cauchy sequence. -/ theorem aux_hasSum_of_le_geometric : HasSum (fun n : β„• ↦ C * r ^ n) (C / (1 ...
4,866
lean_file_chunk
3b38c520a0186c26fbd224c8f431c47b9a8254799f9d817c0334ad25acf151d9
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 RΓ©my Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: RΓ©my Degenne -/ module public import Mathlib.Analysis.SpecificLimits.Basic /-! # Arithmetic-geometric sequences An arithmetic-geometric sequence is a sequence defined by the recurrenc...
14,079
lean_file_chunk
053241626c42aa3bb7b06927f099bc323f087be8dc866d602622a8c4bfe0c372
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Algebra.Order.Field.GeomSum public import Mathlib.Analysis.SpecificLimits.Basic public import Mathlib.Analysis.SpecialFunctions.Po...
18,576
lean_file_chunk
29d704ef9c408223897ded96680fdae10c4cb57887251c1fe41b94974b305396
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Michael Stoll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Stoll -/ module public import Mathlib.Analysis.Normed.Field.WithAbs public import Mathlib.Analysis.SpecialFunctions.Pow.Real /-! # Equivalence of real-valued absolute values ...
6,485
lean_file_chunk
b3d57c00ad03dd43e037700948b4dfd6ea2af358afa090f8b1b9a28a3a278bdf
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Winston Yin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Winston Yin -/ module public import Mathlib.Analysis.ODE.Basic public import Mathlib.Analysis.Calculus.FDeriv.Add public import Mathlib.Analysis.Calculus.FDeriv.Equiv public import Mathl...
5,488
lean_file_chunk
e66a412d524d1d11863c9a95d4cd261612cf5720090a9cf92e16af1201c2975a
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Winston Yin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Winston Yin -/ module public import Mathlib.Analysis.Calculus.Deriv.Basic /-! # Integral curves of vector fields on a normed vector space Let `E` be a normed vector space and `v : ℝ β†’ ...
23,995
lean_file_chunk
04b23132581d9de38747f1bd7b4a8962c77e185d71c601b67588eb929c03a7e9
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, Winston Yin -/ module public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic public import Mathlib.Topology.Algebra.Order.Floor public import Mathlib.Topolo...
18,180
lean_file_chunk
21b35c4d1252033849aea7500f197decc810c9a0a54e679aedf78df34747cd2b
lean_source_file
pkg_mathlib_source_file_chunks
(hmem : βˆ€ t ∈ Icc tmin tmax, Ξ± t ∈ u) (xβ‚€ : E) {t : ℝ} (ht : t ∈ Icc tmin tmax) : HasDerivWithinAt (picard f tβ‚€ xβ‚€ Ξ±) (f t (Ξ± t)) (Icc tmin tmax) t := by apply HasDerivWithinAt.const_add have : Fact (t ∈ Icc tmin tmax) := ⟨ht⟩ -- needed to synthesise `FTCFilter` for `Icc` apply intervalIntegral.integral_h...
19,104
lean_file_chunk
0e33e1d3db1cdbe4b93630d95c3213c016dd4051dfa3f30522acb9c1a4fdeddd
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.SpecialFunctions.ExpDeriv /-! # GrΓΆnwall's inequality The main technical result of this file is the GrΓΆnwall-like inequalit...
19,102
lean_file_chunk
b4a6ce96e3e62afdfde63d27343888b1d133260dc9447af32705307342d2e3ce
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.Basic public import Mathlib.MeasureTheory.Integral.Bochner.Set /-! # McShane integrability vs Bochner integrabil...
22,984
lean_file_chunk
f87ec0e876ba447ca3aa9ba0c686143738271b7803f22ad89bea27c1e19e16eb
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 Xavier Roblot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Xavier Roblot -/ module public import Mathlib.Algebra.Module.ZLattice.Basic public import Mathlib.Analysis.BoxIntegral.Integrability public import Mathlib.Analysis.BoxIntegral.Partitio...
23,970
lean_file_chunk
917eea9051edbe6a6a78fd9eb595ae790af1c9ef7dbd0a88493e5517abfd4a66
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.Filter public import Mathlib.Analysis.BoxIntegral.Partition.Measure public import Mathlib.Analysis.Osci...
23,555
lean_file_chunk
9d90d396bca37b3059f6b395f5f2f576e182146d9d8d6aa5857b095b7ce90219
lean_source_file
pkg_mathlib_source_file_chunks
βˆƒ y : F, HasIntegral J l f vol y ∧ Tendsto (integralSum f vol) (l.toFilteriUnion I (Prepartition.single I J hJ)) (𝓝 y) := by refine (cauchy_map_iff_exists_tendsto.1 (h.cauchy_map_integralSum_toFilteriUnion (.single I J hJ))).imp fun y hy ↦ ⟨?_, hy⟩ convert hy.comp (l.tendsto_embedBox_toFilteriUnion_top h...
15,941
lean_file_chunk
02e776beafae2024b4939c60e6a042dc318a2ea78140a72ac014d909a6f31a9b
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.Basic public import Mathlib.Analysis.BoxIntegral.Partition.Additive public import Mathlib.Analysis.Calculus.FDeri...
17,207
lean_file_chunk
48b7ab2ead5cbb8acabfba4cbeab2eab0cdbe102f5498cb519abaa68b074523c
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.Divisor public import Mathlib.Analysis.Meromorphic.IsolatedZeros public import Mathlib.Analysis.Meromorphic.NormalF...
23,957
lean_file_chunk
8359813bb2dcc8328f85d5fbf9a9240072ba7a7d4163c3faeb2e416ebb99c079
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, Stefan Kebekus -/ module public import Mathlib.Analysis.Meromorphic.Basic public import Mathlib.Algebra.Order.WithTop.Untop0 /-! # Orders of Meromorphic Functions Th...
14,997
lean_file_chunk
76f7026c403c5b7c325b2fa89f8a32e34cdee5161c93c241a63439e1d697f19f
lean_source_file
pkg_mathlib_source_file_chunks
simp only [Pi.inv_apply, h₁a hβ‚‚a, smul_eq_mul, mul_inv_rev, zpow_neg] ring /-- The order of a quotient is the difference of the orders. -/ @[to_fun] theorem meromorphicOrderAt_div {f g : π•œ β†’ π•œ} (hf : MeromorphicAt f x) (hg : MeromorphicAt g x) : meromorphicOrderAt (f / g) x = meromorphicOrderAt f x - merom...
23,958
lean_file_chunk
62afbeeceb2b273bc9352d2d1f052f53bf511e6cd80a2a7a4bfe931df51a2ac8
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.Divisor /-! # Normal form of meromorphic functions and continuous extension If a function `f` is meromorphic on `...
5,578
lean_file_chunk
466439575c592ac7a09fdd86e9cd4685d4f6b0ba0317de223f0c3ad078d50467
lean_source_file
pkg_mathlib_source_file_chunks
MeromorphicNFOn (fun x ↦ ∏ i ∈ s, f i x) U := by convert meromorphicNFOn_prod h₁f hβ‚‚f exact (Finset.prod_apply _ s f).symm /-- A finprod of meromorphic functions in normal form is in normal form if at most one of the factors vanishes. -/ theorem meromorphicNFOn_finprod {ΞΉ : Type*} {f : ΞΉ β†’ π•œ β†’ π•œ} (h₁f : βˆ€ i, Mer...
23,975
lean_file_chunk
2d35b7e941b8625dbc4dcff65647c339b5bcd43208709704a6e7f53706df43ec
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, Stefan Kebekus -/ module public import Mathlib.Analysis.Analytic.Order public import Mathlib.Analysis.Analytic.IsolatedZeros public import Mathlib.Analysis.Calculus.De...
4,932
lean_file_chunk
873a953f6b32b0b5da15f2767aa678c7fa65049e2549b52faaae37fa089f42af
lean_source_file
pkg_mathlib_source_file_chunks
(h : MeromorphicOn f U) : ({z | AnalyticAt π•œ f z}ᢜ ∩ U).Countable := by apply (HereditarilyLindelofSpace.isLindelof _).countable_of_isDiscrete (isDiscrete_of_codiscreteWithin _) simpa using eventually_codiscreteWithin_analyticAt f h end MeromorphicOn /-- Meromorphy of a function on all of π•œ. -/ @[fun_pr...
16,054
lean_file_chunk
ded6b878137220c339ce0bd6b1d5b144a2dc2109d06c56556c42b9dc30c4f19b
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.Order /-! # The Trailing Coefficient of a Meromorphic Function This file defines the trailing coefficient of a me...
16,467
lean_file_chunk
2aa3e12e222c1eb4e8ad111ffb615ae70be0a275ceffb8598c7953bf1ade28f1
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.Algebra.Order.WithTop.Untop0 public import Mathlib.Analysis.Meromorphic.IsolatedZeros public import Mathlib.Analysis.Meromorphic.Order p...
817
lean_file_chunk
de43e5f4ec0fd2323086f47a5633af8e86852ad5778ddc3be767357163663bc0
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Miyahara Kō. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Miyahara Kō -/ module public import Mathlib.Analysis.Meromorphic.NormalForm public import Mathlib.Analysis.SpecialFunctions.Gamma.Beta /-! # The Gamma function is meromorphic -/ public...
5,231
lean_file_chunk
a254da8428c56cb84600a426edf79f4d03d2e4bcb2188bcbdfad6872a4b9af97
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.Basic /-! # Principles of Isolated Zeros and Identity Principles for Meromorphic Functions In line with results i...
308
lean_file_chunk
ac4f4e7f4feaacd41143d5e35d1c3346f35192322085e3ad50f35d77a7738890
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.Topology.Algebra.InfiniteSum.Order public import Mathlib.Topology.MetricSpace.Bounded deprecated_module (since := "2025-11-21")
119
lean_file_chunk
af68e3e8e43507c27eea40e225e699382e1d6b57bd3fe9488ad945abffd0235b
lean_source_file
pkg_mathlib_source_file_chunks
module -- shake: keep-all public import Mathlib.Analysis.Normed.Group.Basic deprecated_module (since := "2025-11-21")
270
lean_file_chunk
a60de54923bb8244b07223f0d9e4e9d12975ac70328f80555c036dcb892dbbc9
lean_source_file
pkg_mathlib_source_file_chunks
module -- shake: keep-all public import Mathlib.Algebra.Order.BigOperators.Expect public import Mathlib.Analysis.Normed.Group.Basic public import Mathlib.Data.Real.Sqrt public import Mathlib.Tactic.ContinuousFunctionalCalculus deprecated_module (since := "2025-11-21")
356
lean_file_chunk
69d7810a5526e6a6867e3a55422b62b44495b9edfea1e038eae1f94d9fdb55eb
lean_source_file
pkg_mathlib_source_file_chunks
module -- shake: keep-all public import Mathlib.Algebra.Order.Algebra public import Mathlib.Algebra.Order.Field.Power public import Mathlib.Analysis.Normed.Group.Basic public import Mathlib.Data.EReal.Inv public import Mathlib.Topology.Algebra.InfiniteSum.Order public import Mathlib.Topology.MetricSpace.Bounded depre...
237
lean_file_chunk
a628560476e9cdf45999956bca7efa6858c6ecbac6b1b9b9d3ddea67f2c3f88d
lean_source_file
pkg_mathlib_source_file_chunks
module -- shake: keep-all public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan public import Mathlib.MeasureTheory.Integral.Bochner.Basic public import Mathlib.Tactic.Positivity deprecated_module (since := "2025-11-21")
258
lean_file_chunk
8e7e1c0a03b883fe51fe935a0ebc1fc8a1d07231f7b30b7e04ef4d3236cdda68
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.Operations public import Mathlib.Topology.MetricSpace.Bounded deprecated_module (since := "2025-11-21")
12,430
lean_file_chunk
53fe4fcd35b3d725246e8624c7701a85a1a43b2b7b5016b42fb668719045b3fa
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.LocallyConvex.BalancedCoreHull public import Mathlib.Analysis.Convex.TotallyBounded public import Mathlib.Analysis.LocallyConvex.Boun...
9,714
lean_file_chunk
955562ac915ca1e7424ce10822d30ab703f53b95206c87c41e4c62eef76213ec
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.Normed.Field.Lemmas public import Mathlib.Analysis.LocallyConvex.WithSeminorms public import Mathlib.LinearAlgebra.Dual.Lemmas public...
4,605
lean_file_chunk
01a28fc75bc5a35f57a7a1cd23a37b805213a5456c19054847ffdbdf4de7146d
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ module public import Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM public import Mathlib.Analysis.LocallyConvex.WithSeminorms public import Mathlib.Analys...
11,087
lean_file_chunk
3ae90f9c765b814d8d0a0cfe209585974769ad19c283612b6b544b0c91e2c395
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel, Filippo A. E. Nuccio -/ module public import Mathlib.Algebra.Central.Basic public import Mathlib.Analysis.LocallyConvex.Separation public import Mathlib.Analysis...
9,053
lean_file_chunk
1ae4f7f546b9d3ff0bd9d88c9ef78b676e3f363917f9e5b0355d38b9895c1e18
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, Kalle KytΓΆlΓ€ -/ module public import Mathlib.Analysis.Normed.Module.Basic public import Mathlib.LinearAlgebra.SesquilinearForm.Basic public import Mathlib.Topology.Algebra.M...
12,019
lean_file_chunk
2d17dbe92c2fe8ccb4008b01d91ba7dffbf7cd4ce845693c660a8a1df8d9a7a5
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 FrΓ©dΓ©ric Dupuis. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: FrΓ©dΓ©ric Dupuis -/ module public import Mathlib.Analysis.LocallyConvex.WithSeminorms public import Mathlib.Analysis.LocallyConvex.SeparatingDual public import Mathlib.Topology.Algebr...
12,312
lean_file_chunk
6dfb36feb2a3ca8178ccd28a935984b1537994270976f76f33fb939c89019cac
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 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.LocallyConvex.WithSeminorms public import Mathlib.Topology.Semicontinuity.Basic public import Mathlib.Topology.Baire.Lemmas...
10,074
lean_file_chunk
37816b80e60171eddf51177c3a0f53bc77114623c1fdfb5b06d4222017c39456
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.LocallyConvex.Basic /-! # Balanced Core and Balanced Hull ## Main definitions * `balancedCore`: The largest balanced subset of a s...
11,989
lean_file_chunk
453da2cc29e017ce042d123679a1db5b595c87053b62ff3f648ef6a1afc95e87
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2019 Jean Lo. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jean Lo, Bhavik Mehta, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Convex.Hull public import Mathlib.Analysis.Normed.Module.Basic public import Mathlib.Topology.Bornology.Absorbs /...
2,153
lean_file_chunk
1b444323b594cafdbb4c02d20248ec0a5de90567d10f091337e0ce9a1ad46e35
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker -/ module public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap public import Mathlib.Topology.Algebra.Module.LocallyConvex /-! # Local convexit...
5,648
lean_file_chunk
a8056a9de7d66223c6406a8cb5a2e231df57d27bdec1d3be5ac04935bdbd7969
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 -/ module public import Mathlib.Analysis.LocallyConvex.Bounded public import Mathlib.Analysis.SpecificLimits.Normed /-! # Continuity and Von Neumann boundedness This f...
4,790
lean_file_chunk
6e0b12951257abeb46230ceb8dac3da41279ccb42e4e5ef4edbe1db6482b80ce
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.LocallyConvex.AbsConvex public import Mathlib.Analysis.LocallyConvex.WithSeminorms public import Mathlib.Analysis.Convex.Gauge /-! #...
23,990
lean_file_chunk
1072dcd71bdca17d33bb1915b2ab600c56c0402a3164c02ab3c0759d3920ca3f
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, Anatole Dedecker -/ module public import Mathlib.Analysis.LocallyConvex.Bounded public import Mathlib.Analysis.Seminorm public import Mathlib.Data.Real.Sqrt public import Ma...
23,957
lean_file_chunk
2b5d76ed0b39ff842b3208d69c3f4d421dab26da098b13b0d98db7b5f7760f76
lean_source_file
pkg_mathlib_source_file_chunks
(hp : WithSeminorms p) : IsVonNBounded π•œ (f '' s) ↔ βˆ€ i : ΞΉ, βˆƒ r > 0, βˆ€ x ∈ s, p i (f x) < r := by simp_rw [hp.isVonNBounded_iff_seminorm_bounded, Set.forall_mem_image] theorem WithSeminorms.isVonNBounded_iff_seminorm_bddAbove {s : Set E} (hp : WithSeminorms p) : IsVonNBounded π•œ s ↔ βˆ€ i : ΞΉ, BddAbove (p i ...
210
lean_file_chunk
06008ea5e5021e929be55fde0cd069489e37a2896a8765de9386371b6e9e638e
lean_source_file
pkg_mathlib_source_file_chunks
exact Filter.iInf.isCountablyGenerated _ have : (uniformity E).IsCountablyGenerated := IsUniformAddGroup.uniformity_countably_generated exact UniformSpace.firstCountableTopology E end TopologicalProperties
20,690
lean_file_chunk
1d888f2809b482f3356028a69f875289d8ffe1a68c3d5992670612ed82743ee7
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 Bhavik Mehta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Bhavik Mehta, YaΓ«l Dillies -/ module public import Mathlib.Analysis.Convex.Cone.Extension public import Mathlib.Analysis.Convex.Gauge public import Mathlib.Analysis.Convex.Topology publ...
22,523
lean_file_chunk
3a3e9f2a8f3f0250ffee9d13bf1727b4eb9983f5c7e5ddfeda38d97c5480af2f
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.GroupTheory.GroupAction.Pointwise public import Mathlib.Analysis.LocallyConvex.Basic public import Mathlib.Analysis.LocallyConvex.BalancedCore...
5,006
lean_file_chunk
cf0cadf3d6dc774426faa2b70759ed60e57066da4217739b133758675c455738
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Moritz Doll. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Moritz Doll -/ module public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap public import Mathlib.Topology.Algebra.Module.Spaces.CompactConvergenceCLM public import Ma...
6,933
lean_file_chunk
ced86658259cfb093ad7c6e6689c0c2048a9710d61dfeb974b6b01a7ed52f49c
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.LocallyConvex.Separation public import Mathlib.Analysis.LocallyConvex.SeparatingDual public import Mathlib.LinearAlgebra.Dual.Def...
21,662
lean_file_chunk
48adbbf270b91339707a6b100f69b5ae0aa893d5631af49d8a57df3f9c39f4b7
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2023 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.LineDeriv.Measurable public import Mathlib.Analysis.Normed.Module.FiniteDimension public import Mathlib.MeasureT...
23,964
lean_file_chunk
f03b3d79c6f3ab6a4ea2ee988a5106248bd2dbcbd4975803da99d4b9e1ceed9c
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2022 Kevin H. Wilson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin H. Wilson -/ module public import Mathlib.Analysis.Calculus.MeanValue public import Mathlib.Analysis.Normed.Module.RCLike.Basic public import Mathlib.Order.Filter.Curry /-! # ...
3,144
lean_file_chunk
a9af8cc91fb0c7aeea860aea6355e18f7f338d9ef0815e5c64ec4fb2db923d4b
lean_source_file
pkg_mathlib_source_file_chunks
(hf' : TendstoUniformlyOnFilter f' g' l (𝓝 x)) (hf : βˆ€αΆ  n : ΞΉ Γ— π•œ in l Γ—Λ’ 𝓝 x, HasDerivAt (f n.1) (f' n.1 n.2) n.2) (hfg : βˆ€αΆ  y in 𝓝 x, Tendsto (fun n => f n y) l (𝓝 (g y))) : HasDerivAt g (g' x) x := by -- The first part of the proof rewrites `hf` and the goal to be functions so that Lean -- can recog...
23,972
lean_file_chunk
a3f2bda2a6edba9635ac5ef9c0fb1e29be860b694991b68d3f169a174b497736
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2020 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ module public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv public import Mathlib.Analysis.Calculus.FDeriv.Add public import Mathlib.Analysis.Calc...
2,478
lean_file_chunk
35a4e7cdd02b30810a4735678443b98a2ac1aaf1542701850a0c0cb1b4ee8db3
lean_source_file
pkg_mathlib_source_file_chunks
set_option backward.isDefEq.respectTransparency false in theorem mem_implicitToOpenPartialHomeomorph_source (hf : HasStrictFDerivAt f f' a) (hf' : f'.range = ⊀) : a ∈ (hf.implicitToOpenPartialHomeomorph f f' hf').source := have := FiniteDimensional.complete π•œ F ImplicitFunctionData.pt_mem_toOpenPartialHomeomor...
6,222
lean_file_chunk
afc41a46bbd0c5fe842f79aa0e5a97ae73ce634b25736703f96f43d89cadd0fa
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.Deriv.Slope public import Mathlib.Analysis.Calculus.Deriv.Comp public import Mathlib.Analysis.Calculus.FDeriv.Add pu...
5,762
lean_file_chunk
e0cd060fb8392ca36dacd7d1939421a8bfc3b3bf719161c4419e3f484841a542
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2025 Winston Yin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Winston Yin -/ module public import Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff /-! # Implicit function...
6,204
lean_file_chunk
c944f3038cc9abe431d2935869604c00fb379577f34502519536b0941b273bb4
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.Calculus.ParametricIntegral public import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic /-! # Derivatives of interva...
23,948
lean_file_chunk
bc7ef75fdcedc18116c71e76748cc0035f983922f8490982b176b2ca9ce2c69b
lean_source_file
pkg_mathlib_source_file_chunks
/- Copyright (c) 2024 SΓ©bastien GouΓ«zel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: SΓ©bastien GouΓ«zel -/ module public import Mathlib.Analysis.Calculus.FDeriv.Symmetric /-! # Vector fields in vector spaces We study functions of the form `V : E β†’ E` on a vector s...
12,867
lean_file_chunk
72ecd9514773d428740d0e4482af61f891e7826e0de28dc68ba1e390662450c3
lean_source_file
pkg_mathlib_source_file_chunks
pullbackWithin π•œ f V s = fun x ↦ (fderivWithin π•œ f s x).inverse (V (f x)) := rfl lemma pullback_eq_of_fderiv_eq {f : E β†’ F} {M : E ≃L[π•œ] F} {x : E} (hf : M = fderiv π•œ f x) (V : F β†’ F) : pullback π•œ f V x = M.symm (V (f x)) := by simp [pullback, ← hf] lemma pullback_eq_of_not_isInvertible {f : E β†’ F} {x ...
23,998
lean_file_chunk
8bbacb6c977f9e23258376d7570dcbdb9e78f4e9fe5708581044b1759a4d21d0
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.Algebra.Polynomial.Module.Basic public import Mathlib.Analysis.Calculus.ContDiff.Operations public import Mathlib.Analysis.Calculus.Deriv.Mean...
3,997
lean_file_chunk
7ba3ed24eccdcf14650ff4c9312aca5f7be0c7f3509138e7b8143b85ea880e48
lean_source_file
pkg_mathlib_source_file_chunks
convert this.symm using 1 Β· simp only [sub_self, ne_eq, Nat.add_eq_zero_iff, one_ne_zero, and_false, not_false_eq_true, zero_pow, zero_div, zero_smul, zero_sub, deriv_div_const, Nat.factorial] apply fun (a b c d : F) (_ : b = c) (_ : a = -d) ↦ show a - b = -c - d by grind Β· grind Β· rw [← i...
7,334
lean_file_chunk
8f5e226331ac600ff985df9012f8dbb7aecc42b958a883fac7e5d924c2ab0c94
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.Calculus.FDeriv.Prod public import Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv public import Mathlib.LinearAlgebr...