lean_workbook_plus_4296

⚠️ 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.

prove that $s\geq \sqrt {-{r}^{2}+2\,{R}^{2}+10\,Rr-2\,\sqrt {R \left( R-2\,r \right) ^{3}}}$ in triangle, where $s$ is the semiperimeter

Why this node was retired

The posted statement is

theorem lean_workbook_plus_4296 : ∀ s r R : ℝ, s ≥ Real.sqrt (-r^2 + 2*R^2 + 10*R*r - 2*Real.sqrt (R * (R - 2 * r)^3))   :=  by sorry

The source explicitly assumes a triangle and associated semiperimeter/inradius/circumradius, but the formal theorem quantifies three unrelated reals.

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

Proposed corrected statement

Quantify a nondegenerate Euclidean triangle and define s,r,R from that triangle before asserting the bound.

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.