Prove2Me

A strict quadratic bound from a sum of squares

Proved
WorkbookSource.problem_35638

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 2bc+3(b2+c2)<6 2bc+3(b^2+c^2) <6

Source: InternLM Lean-Workbook, record lean_workbook_35638 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.problem_35638 (a b c: ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c): (a+b)^2+(b+c)^2+(c+a)^2=3 → 2*b*c+3*(b^2+c^2)<6  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35638; Apache-2.0

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