lean_workbook_plus_15276

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

One informal way to see that $m/n < (m+a)/(n+a)$ for $m < n$ and any positive integer $a$ is to think of it like a free throw percentage in basketball (or any equivalent sporting statistic). Suppose someone has made $m$ out of $n$ free throws this season, and they then take and make $a$ more. Then obviously their percentage can only go up.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15276 (m n a : ℕ) (hmn : m < n) (ha : a > 0) : m / n < (m + a) / (n + a)   :=  by sorry

Both ratios use natural division, erasing the percentages.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Cast m,n,a to ℚ or ℝ; for natural m<n and a>0 prove m/n<(m+a)/(n+a).

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.