An asymmetric cubic bound at fixed sum three

Proved

WorkbookSource.plus_73020

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

lean-workbooksource-checked

Let $a,b,c$ be nonnegative real numbers such that $a + b + c = 3$ . Prove that $2 + a + c^2\ge bc^2$

Source: InternLM Lean-Workbook, record lean_workbook_plus_73020 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_73020 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : 2 + a + c^2 ≥ b * c^2   :=  by sorry

Source