A bilinear bound under two quadratic equalities

Proved

WorkbookSource.base_15151

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

lean-workbooksource-checked

Let $a,b,c$ such that: $a^{2}+c^{2}=1$ $b^{2}+2b(a+c)=6$ Prove that: $b(c-a)\le 4$

Source: InternLM Lean-Workbook, record lean_workbook_15151 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15151 (a b c : ℝ) (ha : a^2 + c^2 = 1) (hb : b^2 + 2 * b * (a + c) = 6) : b * (c - a) ≤ 4  :=  by sorry

Source