Consider a distributed computation consisting of n processes P$1,$ P$2,...$Pn$.$ Let S $=\{$C$1,$ C$2,,$ Cn$\}$ be a set of checkpoints where Ci is a checkpoint of process Pi with vector timestamp VTCi $(1$ i $$ n$).$ Define V TS $=$ sup$($V TC$1,$ V TC$2,,$ VTCn $)$ where sup is the component$-$wise maximum operation. i$.$e$.,$

V TS$[$i$]=$ max$($V TC$1[$i$],$ V TC$2[$i$],,$ V TCn $[$i$])$i$.$

Then prove that S is a consistent global checkpoint of the distributed computation if and only if$$

V TS $=($V TC$1[1],$ V TC$2[2],,$ VTCn $[$n$])$