A product bound on the unit sphere

Proved

WorkbookSource.problem_36034

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c,d \in \mathbb{R}$ such that $a^2 + b^2 + c^2 + d^2 = 1$ . Prove that $(1-a)(1-b) \ge cd$ .

Source: InternLM Lean-Workbook, record lean_workbook_36034 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_36034 (a b c d : ℝ) (h : a^2 + b^2 + c^2 + d^2 = 1) :
  (1 - a) * (1 - b) ≥ c * d  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36034; Apache-2.0

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