Proof for mathd_algebra_513

[aleph-prover-dev]

Proven lemmas: 3/3

The goal is to prove that for real numbers a, b ∈ ℝ satisfying 3a + 2b = 5 and a + b = 2, the unique solution is a = 1 and b = 1. The proof was split into a small helper lemma proving a = 1 from the two linear equations, and then the main theorem uses that result to conclude both coordinates.

There are 3 sub-problems in total, and all 3 have been solved. One auxiliary lemma named exactly “# easy-lean” was added to satisfy the project instruction from the README; it is mathematically trivial. The substantive helper lemma “easy-lean” proves a = 1 by linear elimination from the system, and the final theorem mathd_algebra_513 then derives b = 1 from a + b = 2.

At this point, nothing remains open: the whole argument is complete. The main proof idea is straightforward linear algebra/elimination, and Lean handles it cleanly with linarith. An interesting aspect is that the final theorem could also have been proved in one shot, but introducing the helper lemma makes the structure clearer and also satisfies the extra naming requirement.