Prove2Me

Two bounds under a quadratic normalization

Proved
WorkbookSource.problem_15878

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

lean-workbooksource-checked

Let a,b,c∈R+ a,b,c \in R^+ be such that (a+b)2+(b+c)2+(c+a)2=3 (a+b)^2+(b+c)^2+(c+a)^2=3 . prove that 2(b+c)2≤6−(2a+b+c)2≤4(b2+c2) 2(b+c)^2 \le 6-(2a+b+c)^2 \le 4(b^2+c^2)

Source: InternLM Lean-Workbook, record lean_workbook_15878 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_15878 (a b c : ℝ) (h : (a+b)^2 + (b+c)^2 + (c+a)^2 = 3) : 2 * (b+c)^2 ≤ 6 - (2*a + b + c)^2 ∧ 6 - (2*a + b + c)^2 ≤ 4 * (b^2 + c^2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15878; Apache-2.0

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