Prove2Me

A sharp bound with one linear variable

Proved
WorkbookSource.plus_82261

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

lean-workbooksource-checked

Let a,b,c>0a,b,c> 0 and a+b2+c2=4.a+b^2+c^2=4 . Prove that

a2+b2+c2≥154a^2+b^2+c^2 \geq \frac{15}{4}

Source: InternLM Lean-Workbook, record lean_workbook_plus_82261 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.plus_82261 (a b c : ℝ) (ha : a > 0 ∧ b > 0 ∧ c > 0)(hab : a + b^2 + c^2 = 4) : a^2 + b^2 + c^2 ≥ 15 / 4   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_82261; Apache-2.0

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