Prove2Me

A mixed product bound on a sphere

Proved
WorkbookSource.plus_5056

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

lean-workbooksource-checked

3=a2+b2+c2≥2ab+2c+(c−1)2−1→ab+c≤23=a^2+b^2+c^2 \geq 2ab+2c +(c-1)^2-1 \to ab+c \leq 2

Source: InternLM Lean-Workbook, record lean_workbook_plus_5056 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_5056 (a b c : ℝ) (h : 3 = a ^ 2 + b ^ 2 + c ^ 2) : a * b + c ≤ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_5056; Apache-2.0

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