lean_workbook_plus_47184

Proved

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

Prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} \geq a+b+c$ for $a, b, c$ being the lengths of the sides of a triangle.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47184 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a^2 / b + b^2 / c + c^2 / a ≥ a + b + c   :=  by sorry

Source

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

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