A mixed square-cube bound at sum three

Proved

WorkbookSource.problem_45209

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a, b, c\geq 0$ and $a+b+c=3$ .Then

a^2+b^2+c^3\leq 27

Source: InternLM Lean-Workbook, record lean_workbook_45209; Apache-2.0. Complete source proposition preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_45209 (a b c : ℝ) (ha : a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0) (hab : a + b + c = 3) : a ^ 2 + b ^ 2 + c ^ 3 ≤ 27  :=  by sorry

Source