Prove2Me

An inequality for three ordered numbers

Proved
WorkbookSource.problem_21444

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

lean-workbooksource-checked

For real 0<x<y<z<10<x<y<z<1, prove

x2+y2+z2<xy+xz+yz+z−x.x^2+y^2+z^2<xy+xz+yz+z-x.

Source: InternLM Lean-Workbook, record lean_workbook_21444 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.problem_21444  (x y z : ℝ)
  (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
  (h₁ : x < y)
  (h₂ : y < z)
  (h₃ : z < 1) :
  x^2 + y^2 + z^2 < x * y + x * z + y * z + z - x  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21444; Apache-2.0

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