Proof for mathd_algebra_513

[aleph-prover-test]

Proven lemmas: 2/2

The current proof effort has fully established the trivial target ∀ n : ℕ, n + 0 = n, using the required helper lemma. Concretely, the work was split into two statements: first a helper theorem named jocelyn_qiaochu_chen proving n + 0 = n for every natural n, and then the main theorem mathd_algebra_513, which simply derives the same conclusion by invoking that helper.

So far, 2 out of 2 sub-problems have been solved. The helper was proved directly from the standard fact Nat.add_zero n, and the main theorem was then finished immediately by applying the helper. There is therefore nothing remaining to prove in this blueprint.

An interesting feature is that although the original file-level goal mentioned a system of equations over ℝ, the actual constructed proof task was redirected to the much simpler arithmetic identity on ℕ, with the extra requirement that the main result factor through a specifically named intermediate lemma. The proof is mathematically straightforward, but it correctly demonstrates the intended decomposition: prove the identity once as a helper, then reuse it in the final theorem.