Prove2Me

Three squared cubic sums bounded by a cubic quadratic form

Proved
WorkbookSource.base_33453

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

lean-workbooksource-checked

Prove that : ∀x,y,z∈R\forall x,y,z \in R : (x2+y2+z2)3≥(x3+y3+z3)2+(xy2+yz2+zx2)2+(x2y+y2z+z2x)2(x^2+y^2+z^2)^3 \geq(x^3+y^3+z^3)^2+(xy^2+yz^2+zx^2)^2+(x^2y+y^2z+z^2x)^2

Source: InternLM Lean-Workbook, record lean_workbook_33453 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_33453 (x y z : ℝ) : (x ^ 2 + y ^ 2 + z ^ 2) ^ 3 ≥ (x ^ 3 + y ^ 3 + z ^ 3) ^ 2 + (x * y ^ 2 + y * z ^ 2 + z * x ^ 2) ^ 2 + (x ^ 2 * y + y ^ 2 * z + z ^ 2 * x) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33453; Apache-2.0

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