Show that in the centralized algorithm for detecting conjunctive predicates, it is

sufficient for an application process to send the vector clock once after each message is sent

irrespective of the number of messages received. Formally, let first$($s$)$ be true if and only if the

local predicate is true for the first time since the most recently sent message $($or the beginning of

the trace$).$ We say wcp$($s$1,$ s$2,...,$ sn$)$ is true if s$1,$ s$2,...,$ sn are the states in different processes

making the WCP true. Prove the following claim:

$$s$1,...,$ sn : wcp$($s$1,$ s$2,...,$ sn$)$

$$s$$

$1,...,$ s$$

n : wcp$($s$$

$1,$ s$$

$2,...,$ s$$

n$)$i : $1$ i $$ n : first$($s$$

i$)$