A fourth-power pair-sum bound in the unit ball

Proved

WorkbookSource.base_6142

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

lean-workbooksource-checked

prove that: $6\geq{(a+b)^4+(a+c)^4+(a+d)^4+(b+c)^4+(b+d)^4+(c+d)^4}$ for real numbers $a,b,c,d$ satisfying $1\geq{a^2+b^2+c^2+d^2}$

Source: InternLM Lean-Workbook, record lean_workbook_6142 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6142 (a b c d : ℝ) (h : 1 ≥ a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) :
  6 ≥ (a + b) ^ 4 + (a + c) ^ 4 + (a + d) ^ 4 + (b + c) ^ 4 + (b + d) ^ 4 + (c + d) ^ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6142; Apache-2.0

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