A cyclic difference ratio sum with shifted product denominators
ProvedWorkbookSource.base_25671lean-workbooksource-checked
Prove that for all positive real number the inequality
holds.
Source: InternLM Lean-Workbook, record lean_workbook_25671 (Apache-2.0). Complete source proposition preserved; proof developed independently.
Preamble
import Mathlib open Real Nat
Formal statement
theorem WorkbookSource.base_25671 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x - y) / (x * y + 2 * y + 1) + (y - z) / (y * z + 2 * z + 1) + (z - x) / (z * x + 2 * x + 1) ≥ 0 := by sorry
Source