$($Explain Design by Contract in terms of the roles of client and supplier. In [8$[8$ marks]$]$ 

 

the context of Design by Contract, what is the logical relationship between the

contracts in a class and the contracts in any subclass of that class ?$?$

$)$ What is a class invariant? What are consequences for the supplier when speci−[5$-[5$ marks]$]$

fying a public method regarding a class invariant?

For the following lemmas, [12$[12$ marks]$]$

A.($.($A B)−>$)->$ C ($($A −>$->$ B)($)($A −>$->$ C)$)$

B.$.$x($($P($($x)−>$)->$ Q($($x)),$)),$x($($P($($x))$))$x($($Q($($x))$))$

1.$1.$ Use natural deduction proof rules to show validity of each lemma.

2.$2.$ Show relevant Coq tactics for proving each lemma.