`zero_defect_calibrated_implies_cosh`

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module: IndisputableMonolith.Foundation.DAlembert.Stability
domain: Foundation
line: 355 · github
papers citing: none yet

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IndisputableMonolith.Foundation.DAlembert.Stability on GitHub at line 355.

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formal source

 352  exact h_zero_hyp h_zero
 353
 354/-- Zero defect + calibration a = 1 gives H = cosh exactly. -/
 355theorem zero_defect_calibrated_implies_cosh
 356    (H : ℝ → ℝ) (T : ℝ) (hyp : StabilityHypotheses H T)
 357    (h_a1 : hyp.curvature = 1)
 358    (h_zero : UniformDefectBound H T 0)
 359    (h_zero_hyp : ZeroDefectImpliesCoshHypothesis H T hyp) :
 360    ∀ t : ℝ, |t| ≤ T → H t = Real.cosh t := by
 361  intro t ht
 362  have h := zero_defect_implies_cosh H T hyp h_zero h_zero_hyp t ht
 363  simp only [h_a1, Real.sqrt_one, one_mul] at h
 364  exact h
 365
 366end Stability
 367end DAlembert
 368end Foundation
 369end IndisputableMonolith

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