Here is some initial text before the shaded box.


\begin{theorem}
This is the text to be shaded.
\end{theorem}

This is some text after the first shade. It is separated from the environments by a blank line; that is all handled as usual in LATEX.


\begin{cor}
This is more text to be shaded.
It is numbered with the same counter...
...ser asks for a different paragraph indentation inside
the environment.
\end{cor}

Remark   More text. This time not set in shade, however it is numbered in the same sequence.

Finishing text.