Identifying the method of proof

Consider the following proof.

$\begin{aligned}&\text{Prove that } \sqrt{15}+\sqrt{7}>\sqrt{19}.\\&\text{Assume } \sqrt{15}+\sqrt{7}\le\sqrt{19}.\\&\text{Then } \left(\sqrt{15}+\sqrt{7}\right)^2\le 19\\&\qquad 15+2\sqrt{105}+7\le 19\\&\qquad 2\sqrt{105}\le -3\\&\text{hence } \sqrt{15}+\sqrt{7}>\sqrt{19}.\end{aligned}$

This proof can be best described as a