Unit of Integral Domain divides all Elements

Theorem
Let $$\left({D, +, \circ}\right)$$ be an integral domain whose unity is $$1_D$$.

Let $$\left({U_D, \circ}\right)$$ be the group of units of $$\left({D, +, \circ}\right)$$.

Then:
 * $$\forall x \in D: \forall u \in U_D: u \backslash x$$

That is, every unit of $$D$$ is a divisor of every element of $$D$$.

Proof
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