A proof is a "piece of data"? Oh boy. https://en.wikipedia.org/wiki/Proof_theory https://en.wikipedia.org/wiki/Proof_theory https://en.wikipedia.org/wiki/Mode

A proof is a "piece of data"? Oh boy. https://en.wikipedia.org/wiki/Proof_theory https://en.wikipedia.org/wiki/Proof_theory https://en.wikipedia.org/wiki/Model_theory https://en.wikipedia.org/wiki/Model_theory https://en.wikipedia.org/wiki/Mathematical_proof https://en.wikipedia.org/wiki/Mathematical_proof tl;dr: not a piece of data.