You say: "Theorem Y does not state that theorem X is correct. However, theorem Y is used in a proof of theorem X. Therefore, the validity of theorem X depends on the validity of Theorem Y. " Like I said this is flawed from the start. Not only does theorem y not state that x is correct, it doesn't make any statements about x. Also, just because y is used to prove x, doesn't mean it's logical to do so. There are too many puzzle pieces missing to formulate any kind of reasonable theorem. It's not the bible that needs validation, it's the calculator.