\begin{definition}[Definition:Lipschitz Equivalence/Metrics/Definition 2]
Let $M_1 = \struct {A, d_1}$ and $M_2 = \struct {A, d_2}$ be metric spaces on the same underlying set $A$.
Let $\exists K_1, K_2 \in \R_{>0}$ such that:
:$(1): \quad \forall x, y \in A: \map {d_2} {x, y} \le K_1 \map {d_1} {x, y}$
:$(2): \quad \forall x, y \in A: \map {d_1} {x, y} \le K_2 \map {d_2} {x, y}$
Then $d_1$ and $d_2$ are described as '''Lipschitz equivalent'''.
\end{definition}