Lists can be encoded in the lambda calculus. A way to do this, is by defining a lambda term that, like a "cons", inserts an element at the head of a list, initially empty. Rather than showing the full lambda term, we introduce the defined term cons $.$ For example, the result of reducing the encoding of the expression cons $3[7,8]$ will be the encoding for the list $[3,7,8].$ Assume that you have available the fixed$-$point operator Y and the terms cons $,$ sqr and succ $,$ respectively for list construction, square and successor functions. Which expressions will these terms define? Show your argument before the final answer.

$1.$ Y$\backslash$lambda l$.($consxl$)$

$2.$ Y$(\backslash$lambda f$.\backslash$lambda n$.($cons$($sqrn$)($f$($succn$))))0$