Unity Divides All Elements

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

Then unity is a divisor of every element of $$D$$:


 * $$\forall x \in D: 1_D \backslash x$$

Proof 1
The element $$1_D$$ is the unity of $$\left({D, +, \circ}\right)$$, and so:
 * $$1_D \in D: x = 1_D \circ x$$

The result follows from the definition of divisor

Proof 2
This is a special case of Every Unit Divides Every Element, as Unity is a Unit.