Prove2Me

A product bound with positive unit sum

Proved
WorkbookSource.plus_69473

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

lean-workbooksource-checked

If a+b+c=1a+b+c=1 where ( a,ba, b and cc are positive real numbers. Prove that a2+4bc≤1a^2+4bc\le 1

Source: InternLM Lean-Workbook, record lean_workbook_plus_69473 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.plus_69473 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 1) : a^2 + 4 * b * c ≤ 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_69473; Apache-2.0

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