@@ -35,8 +35,13 @@ We collect here some important and frequently used derived proof rules.
\infer{}
{\prop\proves\later\prop}
\infer{}
{\TRUE\proves\plainly\TRUE}
\end{mathparpagebreakable}
Noteworthy here is the fact that $\prop\proves\later\prop$ can be derived from Löb induction, and $\TRUE\proves\plainly\TRUE$ can be derived via $\plainly$ commuting with universal quantification ranging over the empty type $0$.
\subsection{Persistent assertions}
We call an assertion $\prop$\emph{persistent} if $\prop\proves\always\prop$.
These are assertions that ``don't own anything'', so we can (and will) treat them like ``normal'' intuitionistic assertions.