-- Maclain Hunter: Four Proofs (4P)
-- Exact authored source SHA-256: 81c9017e1f76d7211ebd691bf5fddf67038d86d994d408a64b382cf885b26449
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

theorem inference_2 (v0 v1 v2 : Bool) :
    ((!((v0 && ((!v0) || v1)) && ((!v1) || v2))) || ((v0 && v1) && v2)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> decide
#print axioms inference_2

theorem inference_4 (v0 v1 v2 v3 : Bool) :
    ((!(((v0 && v1) && v2) && v3)) || ((v0 && v1) == (v2 && v3))) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide
#print axioms inference_4

theorem inference_5 (v0 v1 v2 v3 : Bool) :
    ((!(((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3))) || ((v0 && v1) && (v2 && v3))) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide
#print axioms inference_5

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

end HunterAuthored