lean_workbook_plus_64602

Proved

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

Given $a, b, c > 0$ and $a^2 + b^2 - ab = c^2$ . Prove that $(a - c)(b - c) \leq 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64602 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a^2 + b^2 - a * b = c^2) : (a - c) * (b - c) ≤ 0   :=  by sorry

Source

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

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