lean_workbook_plus_18941

Proved

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

Let $x = \ln a, y = \ln b, z = \ln c$ are positive reals with $z > y > x$ . We wish to show $\frac{z-y}{x}+\frac{x-z}{y}+\frac{y-x}{z}> 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18941 (x y z : ℝ) (h₁ : 0 < x ∧ 0 < y ∧ 0 < z) (h₂ : z > y) (h₃ : y > x) : (z - y) / x + (x - z) / y + (y - x) / z > 0   :=  by sorry

Source

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

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