\begin{sequent}
\begin{align*}
  \alpha:\Mor ~|~ \HasFullDomain( \alpha ), \HasFullCodomain( \alpha ) \vdash \IsHonest( \alpha )
\end{align*}
\end{sequent}

\begin{sequent}
\begin{align*}
  \alpha:\Mor ~|~ \IsHonest( \alpha ) \vdash \HasFullDomain( \alpha )
\end{align*}
\end{sequent}

\begin{sequent}
\begin{align*}
  \alpha:\Mor ~|~ \IsHonest( \alpha ) \vdash \HasFullCodomain( \alpha )
\end{align*}
\end{sequent}
