-- Maclain Hunter: The Rule(s) of Logic and Logic Applied to Logic, Science, and Proof by Maclain Hunter
-- Exact authored source SHA-256: 9a721430954eafb053405f7db703d2158b367d1000a39c0598cf1e3e3b8f913a
-- 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 inference_7 (v0 v1 v2 v3 v4 v5 v6 : Bool) :
    ((!((((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!v3) || v4)) && ((!v4) || v5)) && ((!v5) || v6))) || (((((v0 && v1) && (v2 && v3)) && v4) && v5) && v6)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> cases v6 <;> decide
#print axioms inference_7

theorem inference_8 (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_8

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

end HunterAuthored