Proof for mathd_algebra_513 - #204
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Proven lemmas: 1/1
The current goal is to prove that the real numbers a and b satisfying 3a + 2b = 5 and a + b = 2 must be exactly a = 1 and b = 1. Mathematically, this is just solving a 2×2 linear system and showing the unique solution is (1,1).
The proof was split into the two conjuncts of the conclusion: first prove a = 1, then prove b = 1. Both of these subgoals are already solved, so progress is 1 theorem completed out of 1 total statement, with 2 out of 2 conjunctive subgoals discharged inside it.
The main strategy is very direct: use the two linear equations together and let Lean’s linear arithmetic tactic derive each equality. A manual version of the same argument is to subtract 2(a + b = 2) from 3a + 2b = 5 to get a = 1, and then substitute into a + b = 2 to get b = 1.
So at this point, nothing substantial remains mathematically: the theorem is essentially finished. The only notable feature is that the proof is especially short because linear arithmetic is enough to solve the system automatically.