Integer is Coprime to 1

Theorem
Every integer is coprime to $1$.

That is:
 * $\forall n \in \Z: n \perp 1$

Proof
Follows from the definitions of coprime and greatest common divisor as follows.

When $n \in \Z: n \ne 0$ we have:
 * $\gcd \left\{{n, 1}\right\} = 1$

Then by definition again:
 * $\gcd \left\{{n, 0}\right\} = n$

and so when $n = 1$ we have $\gcd \left\{{1, 0}\right\} = 1$.