New simple theorem in my book

I added to my online research book the following theorem:

Theorem Let \mathfrak{A} be a distributive lattice with least element. Let a,b\in\mathfrak{A}. If a\setminus b exists, then a\setminus^* b also exists and a\setminus^* b=a\setminus b.

The user quasi of Math.SE has helped me with the proof.

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