Euclidean Metric on Real Number Line is Metric/Proof 2

Proof
Consider the real number line under the Euclidean metric:
 * $M = \struct {\R, d}$

where $d$ is the distance function given by:
 * $\map d {x, y} = \size {x - y}$

Proof of
So holds for $d$.

Proof of
So holds for $d$.

Proof of
So holds for $d$.

Proof of
So holds for $d$.