lean_workbook_plus_50564

⚠️ 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.

Let $a$ , $b$ , and $c$ be prime numbers. Show that $\dfrac32<\dfrac{a+b+c}{2}<\dfrac{5}{2}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_50564 (a b c : ℕ) (ha : a.Prime) (hb : b.Prime) (hc : c.Prime) : 3 / 2 < (a + b + c) / 2 ∧ (a + b + c) / 2 < 5 / 2   :=  by sorry

The source interval is already impossible since each prime is at least2, independently of natural-division mistyping.

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

Proposed corrected statement

Use real division and replace the impossible upper bound by the actual lower bound(a+b+c)/2≥3; there is no uniform upper bound for arbitrary primes.

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.