lean_workbook_plus_18178

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove or disprove: If $x,y,z$ are the sides of a triangle then $x^3+y^3+z^3+2xyz\ge x^2(y+z)+y^2(x+z)+z^2(y+x)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18178 {x y z : ℝ} (hx : 0 < x ∧ 0 < y ∧ 0 < z) (hx1 : y + z > x) (hx2 : z + x > y) (hx3 : x + y > z) : x ^ 3 + y ^ 3 + z ^ 3 + 2 * x * y * z ≥ x ^ 2 * (y + z) + y ^ 2 * (z + x) + z ^ 2 * (x + y)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph