points$)$ MST satisfies the greedy choice property: for any graph G $=($V$,$E$),$ let S C V be any subset

of vertices, if $($u$,$ v$)$ E is the least$-$weight edge connecting S to V $-$ S$,$ then $($u$,$ v$)$ must be in the MST$.$

Kruskal's algorithm first makes disjoint sets for all vertices, then processes all edges in the increasing order of weights, when $($u$,$ v$)$ is processed, if u and v are not in the same set yet, then $($u$,$ v$)$ is added to the MST$,$ and their sets are merged. Please use MST$\text{'}$s greedy choice property to prove that this is correct.