\subsubsection{IMP Proofs}
\begin{examdetails}
    Typically, the exam contains some operational semantics tasks,
    rarely proofs of properties of IMP.
\end{examdetails}
The property proofs can be acheived either using a direct proof of the implication, or using an induction proof.
The latter of which is more common and we typically define $P$ in such a way that we bind everything apart from variables, natural numbers and constant values
using quantifiers, then prove $\forall n \in \N . P(n)$, if we have a free natural numbers.
Before the definition of $P$ we typically state ``Let $<$variables, constants$>$ be arbitrary'', as with any induction proof.