A product of three affine forms on the unit circle

Proved

WorkbookSource.base_10868

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

lean-workbooksource-checked

Let $a,b$ be reals such that $a^2+b^2=1.$ Prove that

(3a+4b)(5a+4)(5b+3) \geq 0

Source: InternLM Lean-Workbook, record lean_workbook_10868 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10868 (a b : ℝ) (h : a ^ 2 + b ^ 2 = 1) : (3 * a + 4 * b) * (5 * a + 4) * (5 * b + 3) ≥ 0  :=  by sorry

Source