lean_workbook_plus_49815

Proved

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

When $a\geq b\geq c$ or $b\geq c\geq a$ or $c\geq a\geq b$ we have that $(a-b)(b-c)(c-a)\leq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49815 (a b c : ℝ) (h : a ≥ b ∧ b ≥ c ∨ b ≥ c ∧ c ≥ a ∨ c ≥ a ∧ a ≥ b) : (a - b) * (b - c) * (c - a) ≤ 0   :=  by sorry

Source