Proof for mathd_algebra_513

[aleph-prover-test]

Proven lemmas: 2/2

The original benchmark goal mentioned a real-number system, but the current proof task has been reduced to the simpler statement ∀ n : ℕ, n + 0 = n. To satisfy the task requirements, the proof was split into two parts: first a helper lemma named jocelyn_qiaochu_chen proving n + 0 = n, and then the main theorem mathd_algebra_513, which reuses that helper.

So far, both sub-problems have been solved: 2 out of 2 are complete. The helper lemma is proved directly using the standard library fact Nat.add_zero, and the main theorem is then proved immediately by invoking the helper on n. This is mathematically straightforward, but the interesting constraint was not the arithmetic itself; it was organizing the proof so that the main theorem genuinely factors through the required helper lemma.

At this point, nothing remains to be proved in the current blueprint. The proof is complete, correct, and uses a clean minimal strategy rather than a more elaborate induction argument.