IndisputableMonolith.Foundation.UniversalForcing.ContinuousRealization

   1import IndisputableMonolith.Foundation.UniversalForcing
   2
   3/-!
   4  ContinuousRealization.lean
   5
   6  The continuous positive-ratio realization is the already-existing
   7  `LogicRealization.ofPositiveRatioComparison` wrapper, re-exported under the
   8  Universal Forcing namespace used by the program paper.
   9-/
  10
  11namespace IndisputableMonolith
  12namespace Foundation
  13namespace UniversalForcing
  14namespace ContinuousRealization
  15
  16open LogicAsFunctionalEquation
  17
  18/-- Continuous positive-ratio Law-of-Logic realization. -/
  19noncomputable def continuousRealization
  20    (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  21    LogicRealization :=
  22  LogicRealization.ofPositiveRatioComparison C h
  23
  24/-- The continuous realization carries the universal forced arithmetic. -/
  25noncomputable def continuous_arith_equiv_logicNat
  26    (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  27    (arithmeticOf (continuousRealization C h)).peano.carrier
  28      ≃ ArithmeticFromLogic.LogicNat :=
  29  (continuousRealization C h).orbitEquivLogicNat
  30
  31end ContinuousRealization
  32end UniversalForcing
  33end Foundation
  34end IndisputableMonolith
  35