A product of shifted squares with symmetric corrections

Proved

WorkbookSource.plus_28064

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

lean-workbooksource-checked

Prove that $(a^2+1)(b^2+1)(c^2+1)+(1+abc)(a^2+b^2+c^2)+abc\ge 15$ given $a,b,c\ge 0$ and $a+b+c=3$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_28064 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_28064 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) + (1 + a * b * c) * (a^2 + b^2 + c^2) + a * b * c ≥ 15   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_28064; Apache-2.0

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