lean_workbook_plus_82391

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

proofwiki

Let $R$ be a commutative ring, $I,J$ are ideals of $R$ such that $I+J=R$ . Show that $IJ=I \cap J$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82391 (R : Type*) [CommRing R] (I J : Ideal R) (h : I + J = ⊤) : I * J = I ⊓ J   :=  by sorry

Source