-- Maclain Hunter: Dynamic Universal Proof (Theorem of Logos)
-- Exact authored source SHA-256: 3211b94553de18d44a03499c2520280e79bdce290d4514c484e07bde354de1b1
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

structure LogicalGround where
  identity : ∀ (α : Type), ∀ a : α, a = a
  noncontradiction : ∀ p : Prop, p → (p → False) → False
  implication : ∀ p q : Prop, p → (p → q) → q
  excludedMiddle : ∀ b : Bool, b = true ∨ b = false
def constructiveLogos : LogicalGround where
  identity := fun _ _ => rfl
  noncontradiction := fun _ hp hn => hn hp
  implication := fun _ _ hp h => h hp
  excludedMiddle := fun b => by cases b; exact Or.inr rfl; exact Or.inl rfl
def necessary {World : Type} (access : World → World → Prop) (claim : World → Prop) (w : World) :=
  ∀ v : World, access w v → claim v
theorem logical_ground_necessary_existence {World : Type} (access : World → World → Prop)
    (w : World) (_unfixed : List Prop) :
    necessary access (fun _ => Nonempty LogicalGround) w :=
  fun _ _ => ⟨constructiveLogos⟩
#print axioms logical_ground_necessary_existence

end HunterAuthored