-- Maclain Hunter: Seven Cycle Logic Completeness
-- Exact authored source SHA-256: 654f95901f1705d915a4354df1489a5498c1c8950014548c0ac177e91e874e61
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

def cycleSigned (b : Bool) : Int := if b then 1 else -1
structure ValidCycleUnit where
  value : Int
  state : Bool
  depth : Nat
  coherent : Bool
  lawful : Bool
  logosCoherence : coherent = true
  logosLawful : lawful = true
def sevenChecks (u : ValidCycleUnit) : Prop :=
  u.value = u.value ∧
  ¬(cycleSigned u.state = 1 ∧ cycleSigned u.state = -1) ∧
  (cycleSigned u.state = 1 ∨ cycleSigned u.state = -1) ∧
  (u.coherent = true ∧ u.lawful = true) ∧
  cycleSigned u.state = cycleSigned u.state ∧
  (cycleSigned u.state = 1 ∨ cycleSigned u.state = -1) ∧
  0 ≤ u.depth
theorem valid_unit_seven_checks (u : ValidCycleUnit) : sevenChecks u := by
  refine ⟨rfl, ?_, ?_, ⟨u.logosCoherence, u.logosLawful⟩, rfl, ?_, Nat.zero_le u.depth⟩
  · cases u.state <;> decide
  · cases u.state
    · exact Or.inr rfl
    · exact Or.inl rfl
  · cases u.state
    · exact Or.inr rfl
    · exact Or.inl rfl
#print axioms valid_unit_seven_checks

theorem source_identity_rule (α : Type) (a : α) : a = a := rfl
#print axioms source_identity_rule

end HunterAuthored