Proof for mathd_algebra_513

[aleph-prover-test]

Proven lemmas: 1/1

The goal is to prove that if real numbers a and b satisfy the linear equations 3·a + 2·b = 5 and a + b = 2, then necessarily a = 1 and b = 1. The proof is split into two subgoals because the conclusion is a conjunction: first prove a = 1, then prove b = 1. In Lean this is done with constructor, which creates exactly these two separate targets.

Both subgoals are then solved using the linarith tactic applied to the given hypotheses h₀ and h₁, which automatically solves linear systems/inequalities over ℝ. So progress is complete: 2 out of 2 subproblems have been discharged, and the theorem is fully proved. Nothing remains to be worked on.

An interesting aspect is that no manual algebraic substitution is needed (though it would work); linarith can directly derive each of a = 1 and b = 1 from the pair of equations, keeping the proof short and robust.