Task $1-$ Even So Soon?

$[16$ pts$]$

For any predicate for which we have a definition, we have rules that allow us to replace the predicate with its definition or vice versa. As an example, consider "Even", defined by Even $)=(2*y).$ We can use this definition via these two rules:

For example, if we know Even$(6)$ holds, then "Def of Even" allows us to infer $)=(2*y.$ On the other hand, if we know that $)=(2*y,$ then "Undef Even" allows us to infer Even$(10).$

In English proofs, we do not distinguish between replacing Even $(x)$ by its definition and vice versa $($both are $"$by the definition of Even"$),$ but in Cozy, you need to say which direction you are doing by using def of Even or undef Even.

We will also need to use Cozy's algebra rule, which lets you infer equations implied by others:

$\backslash$table$[[$Algebra$],[x_1=y_{1}dots{x}_n=y_n$