IndisputableMonolith.NumberTheory.T1BoundaryExclusion

   1import IndisputableMonolith.Unification.UnifiedRH
   2
   3/-!
   4# T1 Boundary Exclusion
   5
   6Extracts the proved theorem that a T1-bounded physically realizable ledger
   7cannot approach the non-existence boundary `x = 0`.
   8-/
   9
  10namespace IndisputableMonolith
  11namespace NumberTheory
  12
  13open IndisputableMonolith.Unification.UnifiedRH
  14
  15/-- A physically realizable ledger cannot approach the T1 boundary. -/
  16theorem realizable_not_boundary_approaching
  17    (sensor : DefectSensor) [PhysicallyRealizableLedger sensor] :
  18    ¬ BoundaryApproaching sensor :=
  19  physicallyRealizableLedger_not_boundaryApproaching sensor
  20
  21/-- Certificate for the T1 boundary exclusion theorem. -/
  22structure T1BoundaryExclusionCert where
  23  no_boundary :
  24    ∀ sensor : DefectSensor, [PhysicallyRealizableLedger sensor] →
  25      ¬ BoundaryApproaching sensor
  26
  27/-- The proved T1 boundary exclusion certificate. -/
  28def t1BoundaryExclusionCert : T1BoundaryExclusionCert where
  29  no_boundary := fun sensor => by
  30    intro
  31    exact realizable_not_boundary_approaching sensor
  32
  33end NumberTheory
  34end IndisputableMonolith
  35