Keltham's treatment of this, to actually be understood, is going to end up requiring:

- The concept of a programminglanguage;
- The concept of a proofsystem that can formally verify things about programs in the programminglanguage;
- And the Assumable Provability Theorem stating that, in most proofsystems, you can freely assume something is provable in order to prove it.

That is, if something is provable within a system, starting from the premise that the quoted statement is provable inside the quoted system, then it's just provable within the system.

Judging by the looks he's currently getting, though, Keltham should maybe back up and talk more about proofsystems and provability first...

Keltham's treatment of this, to actually be understood, is going to end up requiring:

- The concept of a programminglanguage;
- The concept of a proofsystem that can formally verify things about programs in the programminglanguage;
- And the Assumable Provability Theorem stating that, in most proofsystems, you can freely assume something is provable in order to prove it.

That is, if something is provable within a proofsystem, starting from the premise that the quoted statement is provable inside the quoted proofsystem, then it's thereby provable within the system.

Judging by the looks he's currently getting, though, Keltham should maybe back up and talk more about proofsystems and provability and quoting first...

Keltham's treatment of this, to actually be understood, is going to end up requiring:

- The concept of a programminglanguage;
- The concept of a proofsystem that can formally verify things about programs in the programminglanguage;
- And the Assumable Provability Theorem stating that, in most proofsystems, you can freely assume something is provable in order to prove it.

That is, if something is provable within a proofsystem, starting from the premise that the quoted statement is provable inside the quoted proofsystem, then it's thereby provable within the system...