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 |
|---|---|---|---|---|---|
9,175 | lean_file_chunk | dc141ee16326cb2919aebfd6125967daabb3720b68556afc5d6facb16e24fdfb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
public import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
/-!
# A collection of spec... |
23,996 | lean_file_chunk | 1e42debc62544f24f71140406f5844cb7439232562732d3bb310401ffd3dbc56 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
/-!
# Asymptotics
We introduce these relations:
* `IsBigOWith c l f g` : "f is big O of g ... |
23,934 | lean_file_chunk | d9985bf12ceed3418537d2ccbf8009f49cabd7b30bf9bf117812298e29489c10 | lean_source_file | pkg_mathlib_source_file_chunks | IsBigOWith (max c c') (l ⊔ l') f g' :=
IsBigOWith.of_bound <|
mem_sup.2 ⟨(h.weaken <| le_max_left c c').bound, (h'.weaken <| le_max_right c c').bound⟩
theorem IsBigO.sup (h : f =O[l] g') (h' : f =O[l'] g') : f =O[l ⊔ l'] g' :=
let ⟨_c, hc⟩ := h.isBigOWith
let ⟨_c', hc'⟩ := h'.isBigOWith
(hc.sup' hc').isBig... |
13,354 | lean_file_chunk | e2f787fc0edad5c98e7d60c3bf5a63ef2cc3794259e69b1c6108cd36d4012f46 | lean_source_file | pkg_mathlib_source_file_chunks | theorem isBigO_self_const_mul' {c : R} (hc : IsUnit c) (f : α → R) (l : Filter α) :
f =O[l] fun x => c * f x :=
let ⟨u, hu⟩ := hc
hu ▸ (isBigOWith_self_const_mul' u f l).isBigO
theorem isBigO_self_const_mul {c : S} (hc : c ≠ 0) (f : α → S) (l : Filter α) :
f =O[l] fun x ↦ c * f x :=
(isBigOWith_self_cons... |
23,965 | lean_file_chunk | 33c6c6c536064a3725c20e08a85762c2070522109519f9f83f920f063819e350 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
module
public import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Linear growth
This file defines the linear growth of a sequence `u : ℕ → R`. This notion comes in ... |
5,448 | lean_file_chunk | 0ce2ce082585567b601af1239313bcb53aa7010e2140b117f1fb8f20e78c6212 | lean_source_file | pkg_mathlib_source_file_chunks | have a_a_inv' : a'⁻¹ < a⁻¹ := inv_strictAntiOn (Set.mem_Ioi.2 a_0) (Set.mem_Ioi.2 a_0') a_a'
replace a_v' : ∀ᶠ n : ℕ in atTop, a' * n ≤ v n := by
filter_upwards [eventually_lt_of_lt_liminf a_v', eventually_gt_atTop 0] with n a_vn' n_0
exact (le_div_iff_mul_le (Nat.cast_pos'.2 n_0) (natCast_ne_top n)).1 a_vn'.... |
14,591 | lean_file_chunk | 7bb41e8f2dd031b6ffc67999a0d75dbc7133539b04911c84bf1433325798e55e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
module
public import Mathlib.Algebra.Polynomial.Eval.Defs
public import Mathlib.Analysis.Asymptotics.Lemmas
/-!
# Super-Polynomial Function Decay
This file defines a predi... |
19,151 | lean_file_chunk | e4808ee6b86e45e0a6f7732eb2fa8d2a7a0eed840636a608ad1ecb705848aa35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Damien Thomine. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damien Thomine
-/
module
public import Mathlib.Analysis.Asymptotics.LinearGrowth
public import Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp
/-!
# Exponential growth
This file... |
23,995 | lean_file_chunk | 40ffba225d67e645c946b81a6ae672dfe5506a91665757bec4cf5442b5da77e4 | 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, Eric Wieser
-/
module
public import Mathlib.Analysis.Convex.EGauge
public import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
public import Mathlib.Analysis.Semin... |
10,949 | lean_file_chunk | 765f972ba836ac5f22bb7a70deeda168cbcffc02d1027534dae6a3baa3e2a2f1 | lean_source_file | pkg_mathlib_source_file_chunks | isBigOTVS_neg_right
theorem IsLittleOTVS.neg_right (h : f =o[𝕜; l] g) : f =o[𝕜; l] (-g) :=
h.trans_isBigOTVS (.neg_right .rfl)
@[simp]
theorem isLittleOTVS_neg_right : f =o[𝕜; l] (-g) ↔ f =o[𝕜; l] g :=
⟨fun h ↦ by simpa using h.neg_right, .neg_right⟩
@[simp]
theorem isLittleOTVS_fun_neg_right : f =o[𝕜; l] (... |
8,943 | lean_file_chunk | b646fc892069378d76cf0c6e13bd78275ccc9cfb8357cdbad3bd9dac3d29b893 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Convolution
public import Mathlib.Analysis.Distribution.SchwartzSpace.Fourier
/-! # The Fourier transform of the convolution
In thi... |
15,597 | lean_file_chunk | 93f0a9a6d3de8824186b426109028fb4a2b0dea4f25837f952da989623c4f73f | 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.Fourier.AddCircle
public import Mathlib.MeasureTheory.Integral.Pi
/-!
# Multivariate Fourier series
In this file we define th... |
7,247 | lean_file_chunk | a65f3686118b52c0d6ff975d99183fe3154d75555abd5b6afae9bc8871631b8d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Jakob Stiefel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob Stiefel
-/
module
public import Mathlib.Algebra.MonoidAlgebra.Basic
public import Mathlib.Analysis.Complex.Circle
public import Mathlib.Analysis.InnerProductSpace.Basic
public im... |
23,999 | lean_file_chunk | 22ae68ae304b3cf5373eb9ab7ba972f1b0c6d33411b2ddeffa294ecb43f49d18 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.ExpDeriv
public import Mathlib.Analysis.SpecialFunctions.Complex.Circle
public import Mathli... |
3,375 | lean_file_chunk | f19b1225538718df9ecdf77284431cd13f02aa112922b10e2bc74527b2af6aa4 | lean_source_file | pkg_mathlib_source_file_chunks | simpa using hasDerivAt_fourier T (-n) x
variable {T}
theorem has_antideriv_at_fourier_neg (hT : Fact (0 < T)) {n : ℤ} (hn : n ≠ 0) (x : ℝ) :
HasDerivAt (fun y : ℝ => (T : ℂ) / (-2 * π * I * n) * fourier (-n) (y : AddCircle T))
(fourier (-n) (x : AddCircle T)) x := by
convert (hasDerivAt_fourier_neg T n x)... |
23,922 | lean_file_chunk | b66cc5bf91a06d32903dc76c4fcdb7c97dd4aec1156b0caf2d09112538c034f3 | 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: Alex Kontorovich, David Loeffler, Heather Macbeth, Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Calculus.ParametricIntegral
public import Mathlib.Analysis.Calculus.ContD... |
23,078 | lean_file_chunk | a7b63dd07ce72a6c9b79a0b023eef92b8088cfbc9e76f607125fc354dd0a5621 | lean_source_file | pkg_mathlib_source_file_chunks | lemma integrable_fourierPowSMulRight {n : ℕ} (hf : Integrable (fun v ↦ ‖v‖ ^ n * ‖f v‖) μ)
(h'f : AEStronglyMeasurable f μ) : Integrable (fun v ↦ fourierPowSMulRight L f v n) μ := by
refine (hf.const_mul ((2 * π * ‖L‖) ^ n)).mono' (h'f.fourierPowSMulRight L n) ?_
filter_upwards with v
exact (norm_fourierPowSM... |
23,939 | lean_file_chunk | 2514765dc9f020f7f016ee83564ac897437a003c7a1df12a0d50fa561dd9fe07 | 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.Algebra.Group.AddChar
public import Mathlib.Analysis.Complex.Circle
public import Mathlib.Analysis.Fourier.Notation
public import Mathli... |
2,470 | lean_file_chunk | f09cf757206938fa0c6b7b5210bbda721fdc3db316abdece2af93d9fa21e0669 | lean_source_file | pkg_mathlib_source_file_chunks | /-- The Fourier transform from `L1` functions to bounded continuous functions. -/
def Lp.fourierTransform (f : Lp (α := V) E 1) : V →ᵇ E :=
BoundedContinuousFunction.ofNormedAddCommGroup (𝓕 (f : V → E))
(VectorFourier.fourierIntegral_continuous Real.continuous_fourierChar
(innerSL ℝ).continuous₂ (L1.integrable... |
9,332 | lean_file_chunk | 3e54bdbcef8e402ad9c08b62d9417927c16f03979d3edd41dd2e325813fb04be | 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.Algebra.Module.Equiv.Defs
public import Mathlib.Algebra.BigOperators.Group.Finset.Defs
public import Mathlib.Topology.Algebra.Module.Equiv
/-... |
11,944 | lean_file_chunk | 556fdac08d89264e577dded1c5f5a18492de7a3e072e1a0a20297ee162afc94c | 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.Fourier.AddCircle
public import Mathlib.Analysis.Fourier.FourierTransform
public import Mathlib.Analysis.PSeries
public import ... |
13,973 | lean_file_chunk | e13518629724d5e0d5404ac26f008384b38b1d46e6716892310dd3dd55207071 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 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.Fourier.FourierTransform
public import Mathlib.Analysis.InnerProductSpace.Dual
public import Mathlib.Analysis.InnerProductSpace... |
5,448 | lean_file_chunk | 1c5657678e88aac0630044cc47fcea38611d0c7a0ad720a6dcc88aae284d5bbb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Distribution.TemperedDistribution
public import Mathlib.Analysis.Normed.Operator.Extend
/-!
# The Fourier transform on $L^p$
In th... |
8,595 | lean_file_chunk | f5448ebf330a13a568f18268c703e1f6eacba7b92325611c05a12990f52a545e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Algebra.Group.EvenFunction
public import Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar
public import Mathlib.Analysis.Fourier.... |
9,502 | lean_file_chunk | aac33110ab2199aaca9c0c3ab21aba23b10f02c0b8b7ec2c8a0e1d3395d50f07 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.MeasureTheory.Integral.PeakFunction
public import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
/-!
# Fourier inver... |
10,883 | lean_file_chunk | 6a97abdbeeab5ea9fbe12393fb4771d405ba694f839139605098dd469c220ac8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Algebra.Order.Group.Pointwise.Interval
public import Mathlib.Analysis.SpecificLimits.Basic
public import Mathlib.Data.Rat.Cardinal
p... |
23,971 | lean_file_chunk | bbb3eb5d5998f2750fbcc84b24a6eaaa1ba2980818ce090de3e0ce4d95c54ff2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Abhimanyu Pallavi Sudhir, Violeta Hernández Palacios
-/
module
public import Mathlib.Algebra.Order.Ring.StandardPart
public import Mathlib.Analysis.SpecificLimits.Basic
publ... |
23,963 | lean_file_chunk | a859ecd0ae2ed7655c14beb7b8d663ef8e054ca00f8d2564e9fe3f8a603ba197 | lean_source_file | pkg_mathlib_source_file_chunks | theorem infinitePos_def {x : ℝ*} : InfinitePos x ↔ ∀ r : ℝ, ↑r < x := Iff.rfl
set_option linter.deprecated false in
@[deprecated "`InfiniteNeg` is deprecated" (since := "2026-01-05")]
theorem infiniteNeg_def {x : ℝ*} : InfiniteNeg x ↔ ∀ r : ℝ, x < r := Iff.rfl
set_option linter.deprecated false in
@[deprecated "`Infi... |
2,681 | lean_file_chunk | 24f179b4abe590c28fc4e8147e69222ac328ebc1b7de0621ecddc3c40cfa84ff | lean_source_file | pkg_mathlib_source_file_chunks | @[deprecated "`Infinitesimal` is deprecated" (since := "2026-01-05")]
theorem infiniteNeg_mul_infinitePos {x y : ℝ*} :
InfiniteNeg x → InfinitePos y → InfiniteNeg (x * y) := fun hx hy =>
infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos hx hy.not_infinitesimal (hy 0)
set_option linter.deprecated false in
@[de... |
8,815 | lean_file_chunk | 15ea09ac0fdc9f563cf68742cee2cbe89347eb110e5d5765a0998068555bc760 | 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.Normed.Group.FunctionSeries
public import Mathlib.Analysis.SpecificLimits.Normed
public import Mathlib.Tactic.Rify
public i... |
3,500 | lean_file_chunk | d920ef8f16523bbed3496c7815a0cd716510ba7f16af5d6f4fe682cc8d669673 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
public import Mathlib.Topology.Instances.NNReal.Lemmas
public import Mathlib.Tactic.ContinuousFunct... |
11,206 | lean_file_chunk | 41375a48fb1d07a90065b135c397b8b20b1feb1eec86024a701a16973b15230b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Geometry.Manifold.PartitionOfUnity
public import Mathlib.MeasureTheory.Function.AEEqOfIntegral
/-!
# Functions which vanish as di... |
8,150 | lean_file_chunk | 1d49a4d3a55d6236a346112974e440ed1130ec2667f3bf8e70a117e227c81d7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Distribution.TemperedDistribution
/-! # Support of distributions
We define the support of a distribution, `dsuppo... |
13,665 | lean_file_chunk | dac58974ac636132d784d80f12e9f845a5e223b5fee96ab5cc3498ca4d7d53c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 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.Distribution.FourierMultiplier
public import Mathlib.Analysis.Fourier.LpSpace
/-! # Sobolev spaces (Bessel potential spaces)
In thi... |
133 | lean_file_chunk | 2fc80d8a0b6a27303b1c9721fec9d196b874e995a307f33b54af8936460608ee | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.Distribution.SchwartzSpace.Deriv
deprecated_module (since := "2026-01-19") |
23,976 | lean_file_chunk | f6aa17cb32a21d1c8b8c06880baa76703ca87f21b6beae87b3b4f8f15e3f2645 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Luigi Massacci. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luigi Massacci, Anatole Dedecker
-/
module
public import Mathlib.Analysis.Calculus.LineDeriv.Basic
public import Mathlib.Analysis.Distribution.ContDiffMapSupportedIn
public import Mat... |
2,024 | lean_file_chunk | 10f4a5af28349acfd1cb15d80b8b62e12e4dde3a4fc6f1ad86c89d8e576fb9d6 | lean_source_file | pkg_mathlib_source_file_chunks | (lineDerivCLM 𝕜 v f : 𝓓^{k}(Ω, F)) x = lineDeriv ℝ f x v := by
simp [hk]
lemma lineDerivCLM_apply_of_gt {v : E} (hk : n < k + 1) :
(lineDerivCLM 𝕜 v : 𝓓^{n}(Ω, F) →L[𝕜] 𝓓^{k}(Ω, F)) = 0 := by
ext
simp [not_le_of_gt hk]
variable (𝕜) in
lemma lineDerivCLM_eq_of_scalars (𝕜' : Type*)
[NontriviallyNo... |
9,786 | lean_file_chunk | f2680dfa6fb5de1ff825e19e2dfd8f398da5165bb2884591449e6a30efe064a1 | 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.Distribution.TestFunction
public import Mathlib.Topology.Algebra.Module.Spaces.CompactConvergenceCLM
/-!
# Distributions
... |
23,016 | lean_file_chunk | 4fa73f484ea4a4bacddc616288d6d6dc7474806b59a7ca0af313aa9f2ce98670 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff
public import Mathlib.Analysis.Distribution.SchwartzSpace.Fourier
public import Mathlib.MeasureTh... |
244 | lean_file_chunk | 882c7e73cf9a1de05de8444d52cc1bb936dd27c6d7c402a0ef6f772b3c35efb9 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.SpecialFunctions.Bernstein
public import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
public import Mathlib.Data.Nat.Factorial.DoubleFactorial
deprecated_module (since := "2026-01-19") |
8,731 | lean_file_chunk | 9553a66cc367271e2523955c46b2047299192b560fc249a49f825e04e1cc156a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.Analysis.Distribution.TemperedDistribution
/-! # Fourier multiplier on Schwartz functions and tempered distributions
We define a Fourier mul... |
23,933 | lean_file_chunk | 94c9a31325e4dc54f602b312cf1075639be0457273a14986a2345d8c8f6a0d25 | 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, Luigi Massacci
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Operations
public import Mathlib.Topology.ContinuousMap.Bounded.Normed
public import Math... |
12,506 | lean_file_chunk | 31bda587c76abf51c76b3d303b5bb09e0cd9d39701bf7c7a6ae2ce5dee95494e | lean_source_file | pkg_mathlib_source_file_chunks | -- Note: if needed, we could allow an extra parameter `𝕜` in case the user wants to use
-- `structureMapCLM 𝕜 n i`.
theorem continuous_iff_comp {X} [TopologicalSpace X] (φ : X → 𝓓^{n}_{K}(E, F)) :
Continuous φ ↔ ∀ i, Continuous (structureMapCLM ℝ n i ∘ φ) := by
simp [continuous_iInf_rng, continuous_induced_rng... |
23,160 | lean_file_chunk | 21b2a18a143db8f67fd73d3bdce4ea7ffdb038f03628028f80885cb9f553f8a0 | 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, Anatole Dedecker, Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Calculus.ContDiff.Bounds
public import Mathlib.Analysis.SpecialFunctions.JapaneseBracket
public ... |
12,232 | lean_file_chunk | e50ea6f8054ed81cfe8769cc319aac3277ab58a489577ef6a5dcdddfb922e931 | 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.Algebra.Module.Equiv.Defs
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Topology.Algebra.Module.LinearMap
public import Mat... |
14,708 | lean_file_chunk | 95cc36366efd6e2ce342e3089582f525ef506ea2c11ccd3583c3603988596802 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang, Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.Analysis.Normed.Module.B... |
4,522 | lean_file_chunk | 9bad3480ba5d8e5d0eb16c023db753f7bd8533f622883ff9b265969e2b993a90 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.Join
/-!
# Stone's separation theorem
This file proves Stone's separatio... |
14,844 | lean_file_chunk | bdd4c43bb3a467d11d59b5b91a4d84a26bfd2f949de2816833c002e9e4cd5188 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Seminorm
public import Mathlib.GroupTheory.GroupAction.Pointwise
/-!
# The Minkowski functional, normed field version
In th... |
23,929 | lean_file_chunk | 2fcea0fc9bf017fb8f861a20e68c293989ed4643bd382d95604e28ec5705ddd2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Convex.Between
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.Analysis.Normed.Module.Convex
/-!
# Sid... |
23,731 | lean_file_chunk | a93e90c5ede300a42ffd676ee711702a2bf3ef3b298cdaa1911aeba67fb4eff4 | lean_source_file | pkg_mathlib_source_file_chunks | theorem wOppSide_iff_exists_wbtw {s : AffineSubspace R P} {x y : P} :
s.WOppSide x y ↔ ∃ p ∈ s, Wbtw R x p y := by
refine ⟨fun h => ?_, fun ⟨p, hp, h⟩ => h.wOppSide₁₃ hp⟩
rcases h with ⟨p₁, hp₁, p₂, hp₂, h | h | ⟨r₁, r₂, hr₁, hr₂, h⟩⟩
· rw [vsub_eq_zero_iff_eq] at h
rw [h]
exact ⟨p₁, hp₁, wbtw_self_le... |
9,232 | lean_file_chunk | af055c6d140fd9e957273573f0e37e120190050ee279a964e03b4543aa4e11ba | 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.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.Extreme
public import Mathlib.Analysis.Convex.Jensen
public import Mathlib... |
7,947 | lean_file_chunk | 0c4641650e0798afe7adcd8701d60613ede8fa6125040834a1e3f4e1abd1afdc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Kim Morrison
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.LinearAlgebra.AffineSpace.Independent
public import Mathlib.Tactic.FieldSi... |
9,263 | lean_file_chunk | c508dbf2ea5706a143fa767b566baeeeea8de502e43379d1b125636445747359 | 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.Convex.Gauge
public import Mathlib.Analysis.Normed.Module.Convex
/-!
# "Gauge rescale" homeomorphism between convex sets
Giv... |
1,924 | lean_file_chunk | bc5165651aa3fe11aeb2477836ceeb4e9e05e8e05f8946744bea4ff678ef89fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christopher Hoskin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christopher Hoskin
-/
module
public import Mathlib.Topology.UniformSpace.Cauchy
public import Mathlib.Analysis.Convex.Hull
public import Mathlib.Topology.Algebra.IsUniformGroup.Ba... |
13,320 | lean_file_chunk | 457bacb2e85afad2b9ea40f62a5745f85b354c5a3eb36108b8ce22057e81fcab | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Vasily Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasily Nesterov
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Data.Set.Card
public import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional
publ... |
11,013 | lean_file_chunk | e93536bb40db0f11f6d3482845b79bffc18e18613e5fbee3529b57aba4999730 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Antoine Chambert-Loir, Anatole Dedecker
-/
module
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Analysis.Convex.PathConnected
/-!
# Quasiconvex and... |
5,331 | lean_file_chunk | 3c3c5a0ee88f49d86a3f2bed77e692c52da42c287747be14490aee6647a23ec1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.StrictConvexSpace
/-!
# Uniformly convex spaces
This file defines uniformly convex spaces, which are real normed vector sp... |
20,060 | lean_file_chunk | 2bfa52e12e6df8293ce45fac5f38dacde118d75c541874fc3fb1132c46ebc260 | 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.Convex.Function
public import Mathlib.Analysis.Convex.StrictConvexSpace
public import Mathlib.MeasureTheory.Function.AEEqOfIn... |
13,880 | lean_file_chunk | 8cf973fd9cfbf5167dbd974210121def031bf477ab396890147e4a66ea941d49 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yongxi Lin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yongxi Lin
-/
module
public import Mathlib.Analysis.LocallyConvex.Separation
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.Normed.Order.Lattice
import Mathlib.T... |
8,227 | lean_file_chunk | 6ed1fe128134fab97fafc5b4b94fa63e5d7c327beeb7ded36bed5c28b0d6a38d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Paul A. Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul A. Reichert
-/
module
public import Mathlib.Analysis.Convex.Basic
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Topology.MetricSpace.HausdorffDistanc... |
6,535 | lean_file_chunk | 9cf7e6ae8075d14b47424c6667d2eaecefee3b0a13c1b4af8fe365ef21eb93b0 | 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.Convex.Function
/-!
# Convex and concave piecewise functions
This file proves convex and concave theorems for piecewise fun... |
16,453 | lean_file_chunk | 5f84cebd72cf83460701210713710bc70613a9d99c0f1488adda46e3a917964d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set
public import Mathlib.Algebra.Module.LinearMap.Prod
public import Mathlib.Algebra.Order.Module.Sy... |
23,935 | lean_file_chunk | 6132a0abb74ec02b29080479bfc721b5d69403a6aa8704830cab90cf301fc908 | 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, Yury Kudryashov, David Loeffler
-/
module
public import Mathlib.Analysis.Convex.Slope
public import Mathlib.Analysis.Calculus.Deriv.MeanValue
/-!
# Convexity of... |
23,945 | lean_file_chunk | d04b0c7cf8b3771c74b07693a3540aadf52fdecfca918f7fd607dc0ec621a197 | lean_source_file | pkg_mathlib_source_file_chunks | lemma hasDerivWithinAt_sSup_slope_of_mem_interior (hfc : ConvexOn ℝ S f) (hxs : x ∈ interior S) :
HasDerivWithinAt f (sSup (slope f x '' {y ∈ S | y < x})) (Iio x) x := by
have hxs' := hxs
rw [mem_interior_iff_mem_nhds, mem_nhds_iff_exists_Ioo_subset] at hxs'
obtain ⟨a, b, hxab, habs⟩ := hxs'
simp_rw [hasDer... |
3,941 | lean_file_chunk | dca33001486126718a04cf7c5f8707240a48f87bc90debe541ff34558f5a8369 | lean_source_file | pkg_mathlib_source_file_chunks | ### Strict concave functions, derivative at left endpoint of secant
-/
lemma slope_lt_of_hasDerivWithinAt_Ioi (hfc : StrictConcaveOn ℝ S f)
(hx : x ∈ S) (hy : y ∈ S) (hxy : x < y) (hf' : HasDerivWithinAt f f' (Ioi x) x) :
slope f x y < f' := by
simpa only [Pi.neg_def, slope_neg, neg_neg] using
neg_lt_neg... |
23,960 | lean_file_chunk | f1dc750b0c1c78e6fa6de7bf1620764ef65e920ef0d7b486c71d9044ed466ece | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 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.Order.BigOperators.GroupWithZero.Finset
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis.... |
5,482 | lean_file_chunk | 469b48264d7f1bd62451ee09cd57ad9b0d13c99e6dae47fd4c1d0df724be50a5 | lean_source_file | pkg_mathlib_source_file_chunks | · have hx' : x ∈ affineSpan R (range b) := by
rw [b.tot]
exact AffineSubspace.mem_top R E x
obtain ⟨s, w, hw₁, rfl⟩ := (mem_affineSpan_iff_eq_affineCombination R E).mp hx'
refine ⟨s, w, ?_, hw₁, rfl⟩
intro i hi
specialize hx i
rw [b.coord_apply_combination_of_mem hi hw₁] at hx
exact ... |
1,216 | lean_file_chunk | 48675af77f08b814f85cad651e0d360a3445aa94c3d4efe344adfb3f8941394e | 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.Strict
public import Mathlib.Topology.Algebra.Module.Equiv
/-!
# (Pre)images of strict convex sets under continuous l... |
23,996 | lean_file_chunk | 66b840b48abe8a7ed82f5119b92ad41efe46beaea2000d1780ecca3de68737be | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Convex.Topology
public import Mathlib.Analysis.Normed.Module.Ball.Pointwise
public import Mathlib.Analy... |
1,083 | lean_file_chunk | 34a3e24996a38980dec11be4e6702f4c00f6669b519dd8ba4980e5460280b3d4 | lean_source_file | pkg_mathlib_source_file_chunks | LipschitzWith.of_le_add_mul _ fun x y =>
calc
gauge s x = gauge s (y + (x - y)) := by simp
_ ≤ gauge s y + gauge s (x - y) := gauge_add_le hc (this.mono hs) _ _
_ ≤ gauge s y + ‖x - y‖ / r := by grw [gauge_mono this hs (x - y), gauge_ball]; positivity
_ = gauge s y + r⁻¹ * dist x y := by rw ... |
11,866 | lean_file_chunk | a811e3de0eab985e1474628b744a15bcee82269ea75e793ef9a26ac85fdfdd55 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Convex.Hull
/-!
# Extreme sets
This file defines extreme sets and extreme points for sets in a module... |
23,998 | lean_file_chunk | bab8a174d33e8b4057a154dc1db7998d0bdf32fbcd9243d56e0c9d728d086fba | 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, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Nonneg.Ring
public import Mathlib.LinearAlgebra.AffineSpace.Midpoint
public import ... |
2,843 | lean_file_chunk | 6843d2a1906bcc8074d2256f9a04434159f96e61be11286000e48650a1e981df | lean_source_file | pkg_mathlib_source_file_chunks | namespace Prod
variable [Semiring 𝕜] [PartialOrder 𝕜] [AddCommMonoid E] [AddCommMonoid F] [Module 𝕜 E] [Module 𝕜 F]
theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.1 ×ˢ segment 𝕜 x.2 y.2 := by
rintro z ⟨a, b, ha, hb, hab, hz⟩
exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, h... |
23,870 | lean_file_chunk | e95b45cbc86ea3c1b06d460fecaa10064054e43a644f209f484b662d8b7f0bf2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Convex.Strict
public import Mathlib.Analysis.Convex.StdSimplex
public import Mathlib.LinearAlgebra.Affine... |
8,209 | lean_file_chunk | 4c8966f8e494d185b36ae797b766b0f66ea5269d2bf516d36bd549d6502e0344 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Chenyi Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chenyi Li, Ziyu Wang, Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Uniformly and strong... |
8,010 | lean_file_chunk | bee70b12200ed5b5aa8c1c0695401baa43ab020382fa81e88f2541ecae3f0462 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.Extreme
/-!
# Convex independence
This file ... |
11,330 | lean_file_chunk | aaf71e3140b215632b1b9deaea43704fff8c5f3c3de52172d896861752bd0f5c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Convex.Between
public import Mathlib.Data.List.Triplewise
/-!
# Betweenness for lists of points.
This file defines notions of lis... |
9,121 | lean_file_chunk | 7459033c12d4810f7ef0678c027aa30ee6dbe545a3a61f52003961fd27df6730 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Monovary
public import Mathlib.Algebra.Order.Ring.Basic
public import Mathlib.Analysis.Convex.Function
public import Mathlib.T... |
7,862 | lean_file_chunk | 22381a1bfab2d16a1509c9e8749e1dc8015f894615ab1d2f5e171345857de730 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Hull
/-!
# Convex join
This file defines the convex join of two sets. The convex join of `s` and `t` is the union of the
s... |
23,997 | lean_file_chunk | 1213049efa76da8b117177c4a02c9c0ba44eddfac4f5dd1a3ad1638e0695ddd5 | 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, Yaël Dillies
-/
module
public import Mathlib.Algebra.Ring.Action.Pointwise.Set
public import Mathlib.Analysis.Convex.Star
public import Mathli... |
578 | lean_file_chunk | 955d3a44fc26dcf40b4250ac22baf7a12f1b6a48710603689f96d32d4cab1783 | lean_source_file | pkg_mathlib_source_file_chunks | variable [PartialOrder R] [PartialOrder A]
lemma convex_of_nonneg_surjective_algebraMap [FaithfulSMul R A] {s : Set M}
(halg : Set.Ici 0 ⊆ algebraMap R A '' Set.Ici 0) (hs : Convex R s) :
Convex A s := by
simp only [Convex, StarConvex] at hs ⊢
intro u hu v hv a b ha hb hab
obtain ⟨c, hc1, hc2⟩ := halg ha... |
14,838 | lean_file_chunk | 9bba786ea2ba588c8d06942aed3360bf8db40d5783cd1f7a96ec46121b999bef | 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, Malo Jaffré
-/
module
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Tactic.AdaptationNote
public import Mathlib.Tactic.FieldSimp
public import... |
9,649 | lean_file_chunk | f8da73d206a039cc18eca19a20a9e5fd42087e97f204acb96cca2ba3a32c18a2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
module
public import Mathlib.Analysis.Convex.Extreme
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Topology.Algebra.Mo... |
6,753 | lean_file_chunk | a4d784f4c9ed2bdfa4e753c758a268ebd0127b960ca9c42bd8be0d97db21fa59 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Convex.Between
public import Mathlib.Analysis.Convex.StrictConvexSpace
public import Mathlib.Analysis.Normed.Affine.AddTorsor
publi... |
1,580 | lean_file_chunk | aab9f08cd9ab36c2b07ae80d3c1096e3df1047deca381c3e3842076c62b8ad84 | 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.Convex.Function
public import Mathlib.Topology.Algebra.MulAction
import Mathlib.Topology.Algebra.Monoid
/-!
# Topological pr... |
9,829 | lean_file_chunk | f08119b564f56ef7fa688b0b7b24ea6ab35ff9e6b8179f4def412c749ddb0e8b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Algebra.Group.Pointwise.Set.Card
public import Mathlib.Analysis.Convex.Between
public impor... |
5,650 | lean_file_chunk | 377e7fe447a760c1e0c102bb67d0a7ae790d2724776425f0344f5ab6d40a6bec | 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, Floris van Doorn
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Analysis.Normed.Module.Convex
public import Mathlib.Analysis.Normed... |
7,326 | lean_file_chunk | 4e33efef13016db6c0a806da95fa9d7949bfb1b261cba250ff906c73921f5e7f | 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, Yaël Dillies
-/
module
public import Mathlib.Analysis.Convex.Basic
public import Mathlib.Order.Closure
/-!
# Convex hull
This file defines the convex hull of a set... |
23,988 | lean_file_chunk | 042d7f4b767b2cd65ca95eb6c94f747fc9f93f49b60ce05c59c3020a42210e76 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Algebra.Order.Interval.Set.Group
public import Mathlib.Analysis.Convex.Basic
public import Ma... |
20,202 | lean_file_chunk | 44bb1f0452ad00eaaea657d2d7d6743bcb0df90726189c0b2fb3492c6e66ffe0 | lean_source_file | pkg_mathlib_source_file_chunks | constructor
· rintro ⟨w, hw, h01, rfl⟩
have h : w = Finset.affineCombinationLineMapWeights 0 1 (w 1) := by
rw [Fin.sum_univ_two] at hw
ext i
fin_cases i <;> simp [← hw]
rw [h, Finset.univ.affineCombination_affineCombinationLineMapWeights _ (Finset.mem_univ _)
(Finset.mem_univ _)]
e... |
4,161 | lean_file_chunk | 77847520d98aa71a356b2d15e1e662ee1a7bf7bbf27a04dfda31d7a744560a61 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Convex.Basic
public import Mathlib.LinearAlgebra.Projection
public import Mathlib.Topology.Connected.PathConne... |
23,976 | lean_file_chunk | 15d3cf764c8280f2f92fa94f4a77bc7018fab8c5f0ab091a08ac39b367f6e08d | 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, François Dupuis
-/
module
public import Mathlib.Analysis.Convex.Basic
public import Mathlib.Order.Filter.Extr
public import Mathlib.Tactic.NormNum
/-!
# Conve... |
22,153 | lean_file_chunk | a40dc3e3185444f7590f21acb7d48d940fd4cc6772b343d994c83083591d08c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-- The pointwise maximum of strictly convex functions is strictly convex. -/
theorem StrictConvexOn.sup (hf : StrictConvexOn 𝕜 s f) (hg : StrictConvexOn 𝕜 s g) :
StrictConvexOn 𝕜 s (f ⊔ g) :=
⟨hf.left, fun x hx y hy hxy a b ha hb hab =>
max_lt
(calc
f (a • x + b • y) < a • f x + b • f y := h... |
1,483 | lean_file_chunk | 7b0ca7272210488b552068f9ea716b5f4b47232d6c12f29feadb8362fd4b4937 | 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.Convex.Star
public import Mathlib.Topology.Homotopy.Contractible
/-!
# A convex set is contractible
In this file we prove t... |
6,739 | lean_file_chunk | 92245375d978b5a24c982d6634799505c3c459f0edd41f98746542cea079f21b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
module
public import Mathlib.Analysis.Convex.StrictConvexSpace
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.LinearAlgebra.AffineSpace.Simp... |
10,772 | lean_file_chunk | ffb648767f55ad781bae7432e1f0d31da73cc3b2cd1abfca5999f24aa93c0ff0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Module.Convex
public import Mathlib.Analysis.Normed.Module.Ray
public import Mathlib.Analysis.Normed.Module... |
16,996 | lean_file_chunk | 80ffcff0a7e7d66cb4a1c06745c2ddd8aabf1d7116795c3a013404b31247d5aa | 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
-/
module
public import Mathlib.Analysis.Convex.Combination
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Tactic.FieldSi... |
11,279 | lean_file_chunk | 151a02b6839607d2f8e284f84789ece82a49981e1f01261859c86fd037d59b9b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies, Zichen Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Zichen Wang
-/
module
public import Mathlib.Analysis.Normed.Affine.Convex
/-!
# Convex functions are continuous
This file proves that a convex function from... |
4,007 | lean_file_chunk | 4a7f388bbaf2d3f3fba77544715da3ed0e4487b7f687510fef670ea31b4a53e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 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.Convex.Function
public import Mathlib.Topology.Algebra.Affine
public import Mathlib.Topology.Order.LocalExtr
public import Ma... |
4,175 | lean_file_chunk | 6773ac612b0711a722ba7ca7e3b3ef16150b895e1a228fc2f1c7215727f12209 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Affine.AddTorsorBases
public import Mathlib.Analysis.Normed.Module.Convex
public import Mathlib.MeasureTheory.Measure.... |
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