IndisputableMonolith.Foundation.UniversalForcing.Strict.AxiomAudit

   1import IndisputableMonolith.Foundation.UniversalForcing.Strict.Metaphysical
   2import IndisputableMonolith.Foundation.UniversalForcing.Strict.PositiveRatio
   3import IndisputableMonolith.Foundation.UniversalForcing.Strict.DiscreteBoolean
   4
   5/-!
   6  Strict/AxiomAudit.lean
   7
   8  Audit surface for the strict, domain-rich Universal Forcing completion pass.
   9-/
  10
  11namespace IndisputableMonolith
  12namespace Foundation
  13namespace UniversalForcing
  14namespace Strict
  15namespace AxiomAudit
  16
  17open LogicAsFunctionalEquation
  18open Invariance
  19open PositiveRatio DiscreteBoolean Ordered Modular Categorical
  20open Music Biology Narrative Ethics Metaphysical
  21
  22/-! ## Strict universal theorem -/
  23
  24noncomputable example (R S : StrictLogicRealization) :
  25    (StrictLogicRealization.arith R).peano.carrier
  26      ≃ (StrictLogicRealization.arith S).peano.carrier :=
  27  ArithmeticOf.equivOfInitial (StrictLogicRealization.arith R)
  28    (StrictLogicRealization.arith S)
  29-- #print axioms Invariance.strict_universal_forcing
  30--   propext, Quot.sound
  31
  32example (R : StrictLogicRealization) :
  33    ArithmeticOf.PeanoSurface (StrictLogicRealization.arith R) :=
  34  strict_peano_surface R
  35-- #print axioms Invariance.strict_peano_surface
  36--   propext, Quot.sound
  37
  38/-! ## First cross-realization theorem -/
  39
  40noncomputable example (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  41    (StrictLogicRealization.arith (strictPositiveRatioRealization C h)).peano.carrier
  42      ≃ (StrictLogicRealization.arith strictBooleanRealization).peano.carrier :=
  43  ArithmeticOf.equivOfInitial
  44    (StrictLogicRealization.arith (strictPositiveRatioRealization C h))
  45    (StrictLogicRealization.arith strictBooleanRealization)
  46-- #print axioms DiscreteBoolean.strictPositiveRatio_arith_equiv_strictBoolean
  47--   propext, Classical.choice, Quot.sound
  48
  49/-! ## Strict mathematical realizations -/
  50
  51def _ordered_ok :
  52    (StrictLogicRealization.arith strictOrderedRealization).peano.carrier
  53      ≃ ArithmeticFromLogic.LogicNat :=
  54  (StrictLogicRealization.toLightweight strictOrderedRealization).orbitEquivLogicNat
  55
  56def _categorical_ok :
  57    (StrictLogicRealization.arith strictCategoricalRealization).peano.carrier
  58      ≃ ArithmeticFromLogic.LogicNat :=
  59  (StrictLogicRealization.toLightweight strictCategoricalRealization).orbitEquivLogicNat
  60
  61/-! ## Strict domain realizations -/
  62
  63noncomputable def _music_ok :
  64    (StrictLogicRealization.arith strictMusicRealization).peano.carrier
  65      ≃ ArithmeticFromLogic.LogicNat :=
  66  (StrictLogicRealization.toLightweight strictMusicRealization).orbitEquivLogicNat
  67
  68def _biology_ok :
  69    (StrictLogicRealization.arith strictBiologyRealization).peano.carrier
  70      ≃ ArithmeticFromLogic.LogicNat :=
  71  (StrictLogicRealization.toLightweight strictBiologyRealization).orbitEquivLogicNat
  72
  73def _narrative_ok :
  74    (StrictLogicRealization.arith strictNarrativeRealization).peano.carrier
  75      ≃ ArithmeticFromLogic.LogicNat :=
  76  (StrictLogicRealization.toLightweight strictNarrativeRealization).orbitEquivLogicNat
  77
  78def _ethics_ok :
  79    (StrictLogicRealization.arith strictEthicsRealization).peano.carrier
  80      ≃ ArithmeticFromLogic.LogicNat :=
  81  (StrictLogicRealization.toLightweight strictEthicsRealization).orbitEquivLogicNat
  82
  83/-! ## Strict metaphysical package -/
  84
  85noncomputable example (R : StrictLogicRealization) :
  86    (StrictLogicRealization.arith R).peano.carrier ≃ ArithmeticFromLogic.LogicNat :=
  87  (StrictLogicRealization.toLightweight R).orbitEquivLogicNat
  88-- #print axioms Metaphysical.strict_metaphysical_ground_unique
  89--   propext, Quot.sound
  90
  91end AxiomAudit
  92end Strict
  93end UniversalForcing
  94end Foundation
  95end IndisputableMonolith
  96