`AczelSmoothnessPackage`

definition

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module: IndisputableMonolith.Cost.AczelClass
domain: Cost
line: 37 · github
papers citing: none yet

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IndisputableMonolith.Cost.AczelClass on GitHub at line 37.

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depends on

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formal source

  34A concrete `instance` is provided in `IndisputableMonolith.Cost.AczelProof`
  35via the unconditional `dAlembert_contDiff_top` theorem in
  36`IndisputableMonolith.Cost.AczelTheorem`. -/
  37class AczelSmoothnessPackage : Prop where
  38  smooth_of_dAlembert :
  39    ∀ (H : ℝ → ℝ),
  40      H 0 = 1 →
  41      Continuous H →
  42      (∀ t u, H (t + u) + H (t - u) = 2 * H t * H u) →
  43      ContDiff ℝ ⊤ H
  44
  45/-- Smoothness of continuous d'Alembert solutions, parameterized by an
  46`AczelSmoothnessPackage` instance. -/
  47theorem aczel_dAlembert_smooth [AczelSmoothnessPackage] (H : ℝ → ℝ)
  48    (h_one : H 0 = 1)
  49    (h_cont : Continuous H)
  50    (h_dAlembert : ∀ t u, H (t + u) + H (t - u) = 2 * H t * H u) :
  51    ContDiff ℝ ⊤ H :=
  52  AczelSmoothnessPackage.smooth_of_dAlembert H h_one h_cont h_dAlembert
  53
  54end FunctionalEquation
  55end Cost
  56end IndisputableMonolith

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