The Curry-Howard isomorphism states (and this has been proved) that for each formal proof in math, there is a corresponding computer program that halts, and reciprocally.
This means that it is possible to express the proofs of your statements in code.
On the other hand, non-halting programs are AFAIK beyond the reach of formal logic, and as consequence, the set of logical proofs (or more accurately, its isomorphic twin) is a subset of the set of all computer programs.
This means that it is possible to express the proofs of your statements in code.
On the other hand, non-halting programs are AFAIK beyond the reach of formal logic, and as consequence, the set of logical proofs (or more accurately, its isomorphic twin) is a subset of the set of all computer programs.