$K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$

Question

Is it possible to prove the statement

Let $X$ be a topological space. Then $K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$.

based on the following theorem, which I have proven,

Let $X$ be a topological space. Then $X$ is compact iff every net in $X$ has an accumulation point.

as a corollary?

Answer 1

This should just follow from the fact that K is a compact subset of X if and only if K is a compact space under the subspace topology.