-- Maclain Hunter: The Rules of Logic, the Rule of Logic, and Logic Applied to Logic and Science by Maclain Hunter
-- Exact authored source SHA-256: c46dffe19eedddaed435945b17584caa159a9dfd7c87a109cd1bb826010dd286
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

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

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

theorem inference_5 (v0 v1 v2 v3 v4 : Bool) :
    ((!((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!v3) || v4))) || (((v0 && v1) && (v2 && v3)) && v4)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> decide
#print axioms inference_5

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

end HunterAuthored