You are given the following MapSet wrapper arround Dafny's maps, which fixes the type of the "values" to be booleans. As a result, one can think of a MapSet as a set, where an element is considered to be in the MapSet iff it maps to true in the wrapped map.

Implement the following set API calls in terms of this wrapper by invoking Dafny map functions $($given in the image below$).$

The MapSet and the functions needed to be implimented are given here:

datatype MapSet $=$ MapSet $($s : map$)$

predicate member $($m:MapSet, x:T$)\{$

$//$ code this

true

$\}$

function size $($m:MapSet$)$: int $\{$

$//$ code this

$42$

$\}$

function insert $($m:MapSet, x:T$)$: MapSet $\{$

$//$ code this

MapSet $($map$[])$

$\}$

function delete $($m:MapSet, x:T$)$: MapSet $\{$

$//$ code this

MapSet $($map$[])$

$\}$