A quadratic difference bound on a sphere

Proved

WorkbookSource.base_31221

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

lean-workbooksource-checked

Let $a, b, c$ be real numbers such that $a^2+b^2+c^2=3.$ Prove that

a+b+c-(a-b)(a-c)\leq 3

Source: InternLM Lean-Workbook, record lean_workbook_31221 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31221 (a b c : ℝ) (h : a^2 + b^2 + c^2 = 3) :
  a + b + c - (a - b) * (a - c) ≤ 3  :=  by sorry

Source