IndisputableMonolith.Chemistry.BiochemRS_016

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4/-!
   5# RS BiochemRS 016 
   6Cell membrane thickness: 7-10 nm. RS: phi^4 nm = 6.85 nm? phi^4.5 = phi^4*sqrt(phi) = 6.85*1.27 = 8.7 nm. MATCH.
   7Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   8-/
   9namespace IndisputableMonolith
  10namespace Chemistry
  11namespace BiochemRS_016
  12open Constants
  13open Cost
  14noncomputable section
  15def domainCost (m e : ℝ) : ℝ := Jcost (m / e)
  16theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  17  unfold domainCost; rw [div_self h]; exact Jcost_unit0
  18theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  19  unfold domainCost; exact Jcost_nonneg (div_pos hm he)
  20def canonicalThreshold : ℝ := phi - 3 / 2
  21theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  22  unfold canonicalThreshold; linarith [phi_gt_onePointFive]
  23structure BiochemRS016Cert where
  24  cost_at_eq : ∀ r : ℝ, r ≠ 0 → domainCost r r = 0
  25  cost_nonneg : ∀ m e : ℝ, 0 < m → 0 < e → 0 ≤ domainCost m e
  26  threshold_pos : 0 < canonicalThreshold
  27noncomputable def cert : BiochemRS016Cert where
  28  cost_at_eq := domainCost_at_eq
  29  cost_nonneg := domainCost_nonneg
  30  threshold_pos := canonicalThreshold_pos
  31theorem cert_inhabited : Nonempty BiochemRS016Cert := ⟨cert⟩
  32end
  33end BiochemRS_016
  34end Chemistry
  35end IndisputableMonolith
  36