lean_workbook_plus_3450

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that is $a^2+b^2=1$ and $c^2+d^2=1$ then $|ac-bd|\leq1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3450 (a b c d : ℝ) (h1 : a ^ 2 + b ^ 2 = 1) (h2 : c ^ 2 + d ^ 2 = 1) : |a * c - b * d| ≤ 1   :=  by sorry

Source