Proof for mathd_algebra_513 - #209
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Proven lemmas: 1/1
The goal is to prove that if real numbers a, b ∈ ℝ satisfy 3a + 2b = 5 and a + b = 2, then necessarily a = 1 and b = 1.
The proof was split into the two natural subgoals coming from the conjunction: first prove a = 1, and then prove b = 1. Both are straightforward consequences of the given linear equations.
Progress is complete: 2 out of 2 sub-problems have been solved, so the whole theorem is finished. Lean closes each part using linear arithmetic, effectively solving the 2×2 system directly from the hypotheses.
Nothing remains to be proved at this point. The main strategy was to use the fact that the hypotheses form a simple linear system with a unique solution, so a tactic like linarith can derive each variable’s value automatically.