A fourth-power comparison of variables and pair sums

Proved

WorkbookSource.base_11969

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

lean-workbooksource-checked

Let a,b,c be real such that $a+b+c=3$ . Prove that

7(a^4+b^4+c^4)+(a+b+c)^3 \ge (a+b)^4+(b+c)^4+(c+a)^4

Source: InternLM Lean-Workbook, record lean_workbook_11969 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11969 (a b c : ℝ) (h : a + b + c = 3) :
  7 * (a ^ 4 + b ^ 4 + c ^ 4) + (a + b + c) ^ 3 ≥ (a + b) ^ 4 + (b + c) ^ 4 + (c + a) ^ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11969; Apache-2.0

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