lean_workbook_plus_56992

⚠️ 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 $A(0,0)$ be the starting point, $B(x, 4)$ be the point on the river $y = 4$ where you cross, and let $C(8, -7)$ be the ending point. We wish to minimize $|AB| + |BC|$ , which in this case is $\sqrt{x^2 + 16} + \sqrt{(8-x)^2 + 11^2}$ . That's tough to minimize without calculus (probably possible, but not nice).

Why this node was retired

The posted statement is

theorem lean_workbook_plus_56992  (x : ℝ)
  (h₀ : 0 ≤ x ∧ x ≤ 8) :
  Real.sqrt (x^2 + 16) + Real.sqrt ((8 - x)^2 + 11^2) ≥ Real.sqrt (32 + 8^2) + Real.sqrt (18^2 + 11^2)   :=  by sorry

The minimum is17, attained uniquely at x=32/15. Replace the invented radical lower bound by17 and include its attained equality case.

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

Proposed corrected statement

The minimum is17, attained uniquely at x=32/15. Replace the invented radical lower bound by17 and include its attained equality case.

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.