A linear and bilinear bound at fixed squared norm six

Proved

WorkbookSource.plus_49725

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers such that $a^2+b^2+c^2=6$ . Prove that $2a+6b+6c-4bc-3ca\le 19.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_49725 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_49725 (a b c : ℝ) (h : a ^ 2 + b ^ 2 + c ^ 2 = 6) :
  2 * a + 6 * b + 6 * c - 4 * b * c - 3 * c * a ≤ 19   :=  by sorry

Source