A product of three shifted squares is at least sixty-four

Proved

WorkbookSource.base_49081

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

lean-workbooksource-checked

Prove that $(a^2 + 3)(b^2 + 3)(c^2 + 3) \ge 64 \forall a + b + c = 3$

Source: InternLM Lean-Workbook, record lean_workbook_49081 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_49081 (a b c : ℝ) (h : a + b + c = 3) :
  (a^2 + 3) * (b^2 + 3) * (c^2 + 3) ≥ 64  :=  by sorry

Source