Prove2Me

lean_workbook_plus_79828

Proved

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

Prove that ab2+bc2+ca2+6≥3(a+b+c)ab^2 + bc^2 + ca^2 + 6 \geq 3(a + b + c) for a,b,c≥1a, b, c \geq 1.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_79828 (a b c : ℝ) (hab : a ≥ 1) (hbc : b ≥ 1) (hca : c ≥ 1) : a * b ^ 2 + b * c ^ 2 + c * a ^ 2 + 6 ≥ 3 * (a + b + c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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