Proof for mathd_algebra_513 - #193
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Proven lemmas: 1/1
The current goal is to prove that if real numbers a and b satisfy the system 3a + 2b = 5 and a + b = 2, then necessarily a = 1 and b = 1. Mathematically, this is a simple linear-system-solving theorem over ℝ.
The proof was decomposed into two sub-goals: first prove a = 1, then prove b = 1, since the conclusion is a conjunction a = 1 ∧ b = 1. Both parts are handled from the same two hypotheses by linear elimination.
Progress is complete: 2 out of 2 sub-problems are solved. A clean strategy is to take the combination h₀ − 2h₁, which gives a = 1, and then substitute into a + b = 2 to get b = 1. In Lean, this can be discharged directly with constructor followed by linarith on the two equations.
So there is nothing substantial remaining: the theorem is essentially finished and the proposed proof is marked correct. The main interesting point is that the two equations are independent, so they determine a unique solution, making this a textbook use of linear arithmetic automation.