A product of shifted quadratics at fixed sum three

Proved

WorkbookSource.base_40964

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

lean-workbooksource-checked

Prove that $(2a^2+3)(2b^2+3)(2c^2+3) \geq 125$ given $a,b,c \geq 0$ and $a+b+c=3$

Source: InternLM Lean-Workbook, record lean_workbook_40964 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_40964 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab: a + b + c = 3) : (2 * a ^ 2 + 3) * (2 * b ^ 2 + 3) * (2 * c ^ 2 + 3) ≥ 125  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_40964; Apache-2.0

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