lean_workbook_plus_78627

Proved

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

Prove that if $b^2-a^2=d^2-c^2=A$ , then $2(a+b)(c+d)(ac+bd-A)=((a+b)(c+d)-A)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78627 (a b c d A : ℤ) (h₁ : b^2 - a^2 = d^2 - c^2) (h₂ : b^2 - a^2 = A) : 2 * (a + b) * (c + d) * (a * c + b * d - A) = ((a + b) * (c + d) - A)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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