Prove2Me

An absolute difference by cases

Proved
WorkbookSource.problem_40553

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

lean-workbooksource-checked

For real numbers x,yx,y,

∣x−y∣={x−yx>y,y−xx≤y.|x-y|=\begin{cases}x-y&x>y,\\y-x&x\le y.\end{cases}

Source: InternLM Lean-Workbook, record lean_workbook_40553 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_40553 (x y : ℝ) : |x - y| = if x > y then x - y else y - x  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_40553; Apache-2.0

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