A mixed quadratic-quartic lower bound at fixed sum

Proved

WorkbookSource.plus_34885

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

lean-workbooksource-checked

If $a,b,c>0,a+b+c=3$ prove that: $a^2+b^2c^2+10\ge 4(bc+ca+ab)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_34885 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_34885 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^2 + b^2 * c^2 + 10 ≥ 4 * (b * c + c * a + a * b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_34885; Apache-2.0

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