A quartic pairwise-product inequality on a sphere

Proved

WorkbookSource.base_2943

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

lean-workbooksource-checked

Let be a,b,c real numbers if $a^{2}+b^{2}+c^{2}=2$ show that $ab+bc+ca \leq 1+abc(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_2943 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2943 (a b c : ℝ) (h : a ^ 2 + b ^ 2 + c ^ 2 = 2) :
  a * b + b * c + c * a ≤ 1 + a * b * c * (a + b + c)  :=  by sorry

Source