Prove2Me

A rational midpoint lies strictly between its endpoints

Proved
WorkbookSource.problem_12323

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

lean-workbooksource-checked

If α,β\alpha, \beta are rational numbers then α+β2\frac{\alpha+\beta}{2} is also rational. So, if we order the numbers, say α<β\alpha<\beta then:

α<α+β2<β\alpha<\frac{\alpha+\beta}{2}<\beta

Doesn't this qualify?

Source: InternLM Lean-Workbook, record lean_workbook_12323 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_12323 : ∀ {α β : ℚ}, α < β → α < (α + β) / 2 ∧ (α + β) / 2 < β  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12323; Apache-2.0

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