Addition commutes with averaging

Proved

WorkbookSource.problem_43903

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

lean-workbooksource-checked

Prove or disprove the distributive property of addition over averaging: $a+\frac{b+c}{2}=\frac{a+b}{2}+\frac{a+c}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_43903 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_43903 (a b c : ℝ) : a + (b + c) / 2 = (a + b) / 2 + (a + c) / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43903; Apache-2.0

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