IndisputableMonolith.CrossDomain.DevelopmentReversal

   1import Mathlib
   2
   3/-!
   4# C6: Development Reversal — Involution on 2³ Erikson Stages — Wave 62
   5
   6Structural claim: Erikson's 8 life stages form a 2³ tick cycle, and
   7neurodegeneration runs the ladder in reverse. "Reverse" is formalised as
   8an order-reversing involution on `Fin 8`: reverse k = 7 − k.
   9
  10Involution means reverse ∘ reverse = id. The predicted clinical pattern:
  11dementia progression passes through stages in reverse order, with mid-life
  12stages (generativity vs. stagnation) inverting before early ones
  13(trust vs. mistrust).
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.CrossDomain.DevelopmentReversal
  19
  20inductive EriksonStage where
  21  | trustVsMistrust
  22  | autonomyVsShame
  23  | initiativeVsGuilt
  24  | industryVsInferiority
  25  | identityVsConfusion
  26  | intimacyVsIsolation
  27  | generativityVsStagnation
  28  | integrityVsDespair
  29  deriving DecidableEq, Repr, BEq, Fintype
  30
  31theorem eriksonCount : Fintype.card EriksonStage = 8 := by decide
  32theorem erikson_eq_2cube : Fintype.card EriksonStage = 2 ^ 3 := by decide
  33
  34/-- Reversal map on `Fin 8`. -/
  35def reverse : Fin 8 → Fin 8 := fun k => ⟨7 - k.val, by omega⟩
  36
  37/-- Reversal is an involution: reverse ∘ reverse = id. -/
  38theorem reverse_involution (k : Fin 8) : reverse (reverse k) = k := by
  39  apply Fin.ext
  40  simp only [reverse]
  41  omega
  42
  43/-- Reversal swaps first and last. -/
  44theorem reverse_swaps_endpoints :
  45    reverse ⟨0, by decide⟩ = ⟨7, by decide⟩ ∧
  46    reverse ⟨7, by decide⟩ = ⟨0, by decide⟩ := by
  47  refine ⟨?_, ?_⟩
  48  · apply Fin.ext; simp [reverse]
  49  · apply Fin.ext; simp [reverse]
  50
  51/-- Mid-life stages invert before early ones:
  52    reverse of stage 6 (generativity) = stage 1 (autonomy),
  53    reverse of stage 0 (trust) = stage 7 (integrity).
  54    So going in reverse from old-age, we pass stage 6's inverse at
  55    position 1 before stage 0's inverse at position 7. -/
  56theorem midlife_inverts_first :
  57    (reverse ⟨6, by decide⟩).val < (reverse ⟨0, by decide⟩).val := by
  58  simp [reverse]
  59
  60structure DevelopmentReversalCert where
  61  stage_count : Fintype.card EriksonStage = 8
  62  two_cube : Fintype.card EriksonStage = 2 ^ 3
  63  involution : ∀ k : Fin 8, reverse (reverse k) = k
  64  endpoints_swap : reverse ⟨0, by decide⟩ = ⟨7, by decide⟩
  65  midlife_first : (reverse ⟨6, by decide⟩).val < (reverse ⟨0, by decide⟩).val
  66
  67def developmentReversalCert : DevelopmentReversalCert where
  68  stage_count := eriksonCount
  69  two_cube := erikson_eq_2cube
  70  involution := reverse_involution
  71  endpoints_swap := reverse_swaps_endpoints.1
  72  midlife_first := midlife_inverts_first
  73
  74end IndisputableMonolith.CrossDomain.DevelopmentReversal
  75