thm__lattice_theorem_for_substructures.tex

\documentclass{classes/tikzcd}

\begin{document}
  \begin{tikzcd}
    [
      every arrow/.append style={dash, loosely dotted},
      execute at end picture=
     {
       \draw[LightFill, LightDraw] (tikz@f@1-3-1.north west) -- (tikz@f@1-3-1.south west) -- (tikz@f@1-5-3.south west) -- (tikz@f@1-5-3.south east) -- (tikz@f@1-3-5.south east) -- (tikz@f@1-3-5.north east) -- (tikz@f@1-1-3.north east) -- (tikz@f@1-1-3.north west);
     }
    ]
                         &                              & \mscrX                                          &                              &                      &                      &                              & \mscrX / {\cong}                                &                              &                      \\
                         & \Anon \ar[ru]                &                                                 & \Anon \ar[lu]                &                      &                      & \Anon \ar[ru]                &                                                 & \Anon \ar[lu]                &                      \\
    \Anon \ar[ru, solid] & \Anon \ar[ruu]               & \mscrS \ar[lu] \ar[uu] \ar[ru]                  & \Anon \ar[luu]               & \Anon \ar[lu, solid] & \Anon \ar[ru, solid] & \Anon \ar[ruu]               & \mscrS / {\cong} \ar[lu] \ar[uu] \ar[ru]        & \Anon \ar[luu]               & \Anon \ar[lu, solid] \\
                         & \Anon \ar[lu, solid] \ar[ru] &                                                 & \Anon \ar[lu] \ar[ru, solid] &                      &                      & \Anon \ar[lu, solid] \ar[ru] &                                                 & \Anon \ar[lu] \ar[ru, solid] &                      \\
                         &                              & \Anon \ar[lu] \ar[luu] \ar[uu] \ar[ruu] \ar[ru] &                              &                      &                      &                              & \Anon \ar[lu] \ar[luu] \ar[uu] \ar[ruu] \ar[ru] &                              &                      \\
    \Anon \ar[rru]       & \Anon \ar[ru]                & \Anon \ar[u]                                    & \Anon \ar[lu]                & \Anon \ar[llu]       &                      &                              &                                                 &                              &                      \\
                         &                              & \Anon \ar[llu] \ar[lu] \ar[u] \ar[ru] \ar[rru]  &                              &                      &                      &                              &                                                 &                              &
  \end{tikzcd}
\end{document}