[FMFP] Mostly finish exercises section

semester4/fmfp/parts/06_exercises/02_fm/00_imp.tex

@@ -1 +1,9 @@
-\subsubsection{IMP}
+\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.