lean_workbook_plus_30646
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.
by CS : \n \n
\n \n
Why this node was retired
The posted statement is
theorem lean_workbook_plus_30646 : ∀ a b c : ℝ, (a * b * c ≠ 0 ∧ a + b + c ≠ 0) → (a * b / c ^ 2 * (a + b) + b * c / a ^ 2 * (b + c) + c * a / b ^ 2 * (c + a)) * (a + b / a * b + b + c / b * c + c + a / c * a) ≥ (1 / a + 1 / b + 1 / c) ^ 2 := by sorry
Several denominator parentheses are lost: division by c²(a+b) becomes division by c² followed by multiplication, and (a+b)/(ab) also changes.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Restore every source fraction with its full numerator and denominator; impose a,b,c>0 for this Cauchy–Schwarz argument.
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_30646 : ∀ a b c : ℝ, (a * b * c ≠ 0 ∧ a + b + c ≠ 0) → (a * b / c ^ 2 * (a + b) + b * c / a ^ 2 * (b + c) + c * a / b ^ 2 * (c + a)) * (a + b / a * b + b + c / b * c + c + a / c * a) ≥ (1 / a + 1 / b + 1 / c) ^ 2 := by sorry