IndisputableMonolith.Foundation.UniversalForcing.EthicsRealization

   1import IndisputableMonolith.Foundation.UniversalForcing.NarrativeRealization
   2
   3/-!
   4  EthicsRealization.lean
   5
   6  Lightweight ethical realization: the carrier is the count of morally
   7  meaningful improvement steps. The domain theory of ethics is not rebuilt
   8  here; only the identity/step comparison structure needed by Universal
   9  Forcing is formalized.
  10-/
  11
  12namespace IndisputableMonolith
  13namespace Foundation
  14namespace UniversalForcing
  15namespace EthicsRealization
  16
  17open ArithmeticFromLogic
  18open Invariance.Universal
  19
  20abbrev MoralImprovementStep := Nat
  21
  22def ethicsCost (a b : MoralImprovementStep) : Nat :=
  23  if a = b then 0 else 1
  24
  25@[simp] theorem ethicsCost_self (a : MoralImprovementStep) : ethicsCost a a = 0 := by
  26  simp [ethicsCost]
  27
  28theorem ethicsCost_symm (a b : MoralImprovementStep) : ethicsCost a b = ethicsCost b a := by
  29  by_cases h : a = b
  30  · subst h; simp [ethicsCost]
  31  · have h' : b ≠ a := by intro hb; exact h hb.symm
  32    simp [ethicsCost, h, h']
  33
  34def ethicsInterpret (n : LogicNat) : MoralImprovementStep :=
  35  LogicNat.toNat n
  36
  37/-- Ethical realization as morally meaningful improvement count. -/
  38def ethicsRealization : LogicRealization where
  39  Carrier := MoralImprovementStep
  40  Cost := Nat
  41  zeroCost := inferInstance
  42  compare := ethicsCost
  43  zero := 0
  44  step := Nat.succ
  45  Orbit := LogicNat
  46  orbitZero := LogicNat.zero
  47  orbitStep := LogicNat.succ
  48  interpret := ethicsInterpret
  49  interpret_zero := by rfl
  50  interpret_step := by
  51    intro n
  52    show LogicNat.toNat (LogicNat.succ n) = Nat.succ (LogicNat.toNat n)
  53    rfl
  54  orbit_no_confusion := by intro n h; exact LogicNat.zero_ne_succ n h
  55  orbit_step_injective := LogicNat.succ_injective
  56  orbit_induction := by
  57    intro P h0 hs n
  58    exact LogicNat.induction (motive := P) h0 hs n
  59  orbitEquivLogicNat := Equiv.refl LogicNat
  60  orbitEquiv_zero := rfl
  61  orbitEquiv_step := by intro n; rfl
  62  identity := ethicsCost_self
  63  nonContradiction := ethicsCost_symm
  64  excludedMiddle := True
  65  composition := True
  66  actionInvariant := True
  67  nontrivial := by
  68    refine ⟨1, ?_⟩
  69    simp [ethicsCost]
  70
  71noncomputable def ethics_arith_equiv_nat :
  72    (arithmeticOf ethicsRealization).peano.carrier ≃ LogicNat :=
  73  ethicsRealization.orbitEquivLogicNat
  74
  75end EthicsRealization
  76end UniversalForcing
  77end Foundation
  78end IndisputableMonolith
  79