A cubic lower bound with a mixed quadratic constraint

Proved

WorkbookSource.plus_7401

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

lean-workbooksource-checked

Let $a,b,c> 0$ and $a+b^2+c^2=4 .$ Prove that

a+b^2+c^3 \geq \frac{104}{27}

Source: InternLM Lean-Workbook, record lean_workbook_plus_7401 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_7401 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b^2 + c^2 = 4) : a + b^2 + c^3 ≥ 104 / 27   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_7401; Apache-2.0

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