lean_workbook_plus_9048

⚠️ 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.

By Ravi substitution $(a=y+z, b=z+x, c=x+y)$, we get\n $\sum_{cyc}x^7y+3\sum_{cyc}x^7z+\sum_{cyc}x^6y^2+6\sum_{cyc}x^6z^2+5\sum_{cyc}x^6yz+7\sum_{cyc}x^5z^3+13\sum_{cyc}x^5yz^2+2\sum_{cyc}x^4y^4+7\sum_{cyc}x^4yz^3\geq 6\sum_{cyc}x^4y^3z+9\sum_{cyc}x^4y^2z^2+30\sum_{cyc}x^3y^3z^2$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_9048 :
  ∀ x y z : ℝ, (x^7*y + y^7*z + z^7*x) + 3 * (x^7*z + y^7*x + z^7*y) + (x^6*y^2 + y^6*z^2 + z^6*x^2) + 6 * (x^6*z^2 + y^6*x^2 + z^6*y^2) + 5 * (x^6*y*z + y^6*x*z + z^6*x*y) + 7 * (x^5*z^3 + y^5*x^3 + z^5*y^3) + 13 * (x^5*y*z^2 + y^5*z*x^2 + z^5*x*y^2) + 2 * (x^4*y^4 + y^4*z^4 + z^4*x^4) + 7 * (x^4*y*z^3 + y^4*z*x^3 + z^4*x*y^3) ≥ 6 * (x^4*y^3*z + y^4*z^3*x + z^4*x^3*y) + 9 * (x^4*y^2*z^2 + y^4*z^2*x^2 + z^4*x^2*y^2) + 30 * (x^3*y^3*z^2 + y^3*z^3*x^2 + z^3*x^3*y^2)   :=  by sorry

Ravi substitution parameters for triangle sides are positive, but that domain was not retained.

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 x,y,z>0 (or nonnegative for a degenerate extension) and verify the exact degree8 cyclic inequality before using it for the triangle problem.

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.