big data, please finish 2(b)

2. (The Range Query) Given a query range centered at q with radius r and an MBR node e,

2(a). Please provide the pruning condition (i.e., the condition to prune MBR node e) for the range query. [10 points]

Pruning condition: we define d(x,y) as the distance between data node x and data node y

If d(Qr,q)>r(q)+r(Qr)

Then objects in node Qr can be safely pruned

2(b). Please formally prove the pruning condition in 2(a). [10 points]

prove: