-- Maclain Hunter: Logic Says Ergo I Say by Maclain Hunter
-- Exact authored source SHA-256: 4b6e16998317bfdf749f11f102a02813253d6a9845198ef6b2582a08d21dd3b7
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

theorem inference_1 (v0 v1 : Bool) :
    ((!((v0 && (v0 == v1)) && v1)) || (v0 && v1)) = true := by
  cases v0 <;> cases v1 <;> decide
#print axioms inference_1

theorem inference_2 (v0 v1 v2 v3 v4 : Bool) :
    ((!((((v4 && (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_2

theorem inference_3 (v0 v1 : Bool) :
    ((!(v0 && v1)) || (v0 == v1)) = true := by
  cases v0 <;> cases v1 <;> decide
#print axioms inference_3

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

end HunterAuthored