A quartic product bound at fixed squared norm four

Proved

WorkbookSource.base_20423

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

lean-workbooksource-checked

Prove that if $a, b, c, d$ are real numbers such that $a^2 + b^2 + c^2 + d^2 = 4$ , then $3(a^4 + b^4 + c^4 + d^4 + 12abcd) + 80 \geq 8(a + b + c + d)^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_20423 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_20423 (a b c d : ℝ) (h : a^2 + b^2 + c^2 + d^2 = 4) :
  3 * (a^4 + b^4 + c^4 + d^4 + 12 * a * b * c * d) + 80 ≥ 8 * (a + b + c + d)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20423; Apache-2.0

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