Prove2Me

A bilinear inequality on the four-dimensional unit sphere

Proved
WorkbookSource.base_12296

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

lean-workbooksource-checked

For a,b,c,d∈Ra,b,c,d \in \mathbb{R} such that a2+b2+c2+d2=1a^2+b^2+c^2+d^2=1 Prove that a(1+d−a)+b(1+d−b)+c(1+d−c)−d−1≤0a(1+d-a)+b(1+d-b)+c(1+d-c)-d-1 \leq 0

Source: InternLM Lean-Workbook, record lean_workbook_12296 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_12296 (a b c d : ℝ) (h : a^2 + b^2 + c^2 + d^2 = 1) :
  a * (1 + d - a) + b * (1 + d - b) + c * (1 + d - c) - d - 1 ≤ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12296; Apache-2.0

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