lean_workbook_plus_10609

Proved

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

By Cauchy $b^{2}+c^{2}\ge 2bc$ . $f\ge 2(b^{2}c^{2}+a^{2}b^{2}+a^{2}c^{2}-abc(a+b+c)=2(a(b-c)^{2}+b(a-c)^{2}+c(a-b)^{2})\geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_10609  (a b c : ℝ)
  (f : ℝ)
  (h₀ : f = 2 * (b^2 * c^2 + a^2 * b^2 + a^2 * c^2 - a * b * c * (a + b + c)))
  (h₁ : 0 < a ∧ 0 < b ∧ 0 < c)
  (h₂ : a + b > c)
  (h₃ : a + c > b)
  (h₄ : b + c > a) :
  f ≥ 0   :=  by sorry

Source

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

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