Two squares and a cube sum to at least eleven halves at fixed sum four

Proved

WorkbookSource.base_14529

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

lean-workbooksource-checked

Let $a,b,c>0,a+b+c=4 .$ Prove that

a^2+b^2+c^3\geq \frac{11}{2}.

Source: InternLM Lean-Workbook, record lean_workbook_14529 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14529 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 4) : a^2 + b^2 + c^3 ≥ 11 / 2  :=  by sorry

Source