Proof for mathd_algebra_513 - #63
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Proven lemmas: 1/1
The goal is to prove that if real numbers a and b satisfy 3a + 2b = 5 and a + b = 2, then necessarily a = 1 and b = 1. This is a small linear-algebra-style uniqueness argument: the two equations determine the two unknowns.
The proof was decomposed into the two components of the conjunction a = 1 ∧ b = 1. In Lean, that means proving separately that a = 1 and that b = 1 from the given hypotheses.
Progress is complete: 1 out of 1 theorem goals has been solved, and both subgoals inside the conjunction were discharged. The proof uses linarith, which is well suited here because the assumptions and target are all linear equalities over ℝ.
Nothing remains to be proved for this theorem. The key strategy is simply to combine the two equations linearly to isolate each variable, and Lean’s linear arithmetic tactic handles that automatically.