An asymmetric fixed-sum lower bound in mixed powers

Proved

WorkbookSource.plus_12136

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c\geq 0$ and $a+b+c=3.$ Prove that $a^3+ b^2 + c^3+ ab^2c \geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_plus_12136 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_12136 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 3) : a ^ 3 + b ^ 2 + c ^ 3 + a * b ^ 2 * c ≥ 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_12136; Apache-2.0

View graph