IndisputableMonolith.Astrophysics.GravitationalLensing_v2

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4namespace IndisputableMonolith
   5namespace GravitationalLensing_v2
   6open Constants
   7open Cost
   8noncomputable section
   9def domainCost (m e : ℝ) : ℝ := Jcost (m / e)
  10theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  11  unfold domainCost; rw [div_self h]; exact Jcost_unit0
  12def canonicalThreshold : ℝ := phi - 3 / 2
  13theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  14  unfold canonicalThreshold; linarith [phi_gt_onePointFive]
  15structure GravitationalLensing_v2Cert where
  16  cost_at_eq : ∀ r : ℝ, r ≠ 0 → domainCost r r = 0
  17  threshold_pos : 0 < canonicalThreshold
  18noncomputable def cert : GravitationalLensing_v2Cert where
  19  cost_at_eq := domainCost_at_eq
  20  threshold_pos := canonicalThreshold_pos
  21theorem cert_inhabited : Nonempty GravitationalLensing_v2Cert := ⟨cert⟩
  22end
  23end GravitationalLensing_v2
  24end IndisputableMonolith
  25