lean_workbook_plus_41226
Disproved⚠️ Retired — specification defect
The Lean statement below does not encode the problem shown on this page, so its
Disprovedstatus carries no information about that problem. Do not import this node or use it as a dependency.
Prove the inequality \n\n
Why this node was retired
The posted statement is
theorem lean_workbook_plus_41226 : ∀ a b c : ℝ, (a / b) ^ 2 + 2 * (b / c) ^ 2 + (c / a) ^ 2 ≥ (Real.sqrt 5 - 1) * (a / c + c / b + b / a) := by sorry
The formalization totalizes divisions that the ordinary expression leaves undefined.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Require a,b,c nonzero so all source denominators are defined; if the original exercise assumes positivity, state that stronger source domain explicitly.
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.
import Mathlib.Analysis.Complex.Basic
theorem lean_workbook_plus_41226 : ∀ a b c : ℝ, (a / b) ^ 2 + 2 * (b / c) ^ 2 + (c / a) ^ 2 ≥ (Real.sqrt 5 - 1) * (a / c + c / b + b / a) := by sorry