Shading parts of fitch-style natural deduction proofs

Question

I'm using the fitch package (the one written by Prof. Selinger and is now maintained, I believe, by Richard Zach) for pedagogical purposes -- as I suspect many people do.

It would be helpful to be able to highlight parts of proofs with shading. I'm afraid I don't really know how to do that. I know how to put a whole proofs inside a shaded environment, e.g., with the mdframed package.

I've included a MWE for a simple fitch-proof, as well as an image of what I'd like to be able to shade with a box drawn in by hand.

\documentclass{article}

\usepackage{fitch}
\begin{document}

\begin{displaymath}
\begin{nd}
  \hypo {1} {P \lor Q} \by{}{}%
  \hypo {2} {P \rightarrow R} \by{}{}%
  \hypo {3} {Q \rightarrow R} \by{}{}%
  \open%
  \hypo {4} {P} \by{}{}%
  \have {5} {R} \by{}{}%
  \close%
  \open%
  \hypo {6} {Q} \by{}{}%
  \have {7} {R} \by{}{}%
  \close%
  \have {8} {R} \by{}{}%
\end{nd}
\end{displaymath}

\end{document}

Answer 1

You can pretty easily highlight the relevant part of the proof using a box by placing tikzmarks appropriately and drawing a tikzpicture afterwards.

For example,

\documentclass{article}
% ateb: https://tex.stackexchange.com/a/700683/  i gwestiwn Bernhard: https://tex.stackexchange.com/q/700671/    
\usepackage{fitch}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\usetikzlibrary{fit}
\usetikzlibrary{calc}
\begin{document}

\begin{displaymath}
  \begin{nd}
    \hypo {1} {P \lor Q} \by{}{}%
    \hypo {2} {P \rightarrow R} \by{}{}%
    \hypo {3} {Q\tikzmark{a} \rightarrow R} \by{}{}%
    \open 
    \hypo {4} {\tikzmarknode{b}{P}} \by{}{}
    \have {5} {\tikzmarknode{c}{R}} \by{\tikzmarknode{d}{\strut}}{}
    \close
    \open
    \hypo {6} {Q} \by{}{}%
    \have {7} {R} \by{}{}%
    \close
    \have {8} {R} \by{}{}%
  \end{nd}
\end{displaymath}
\begin{tikzpicture}[remember picture,overlay]
  \node [fit=({pic cs:a} |- b) (b) (c) ($(d.south)!.75!(c |- d.south)$),draw=red] {};
\end{tikzpicture}

\end{document}

If you actually want to shade that part of the proof, as opposed to drawing around it, things are considerably trickier. Until the proof is constructed, you don't know where to shade; after it is constructed, you can't easily shade beneath it.

One approach would be to put the proof inside a tikzpicture. Then we can use the backgrounds library to shade the relevant sub-proof after the proof is constructed. For example,

\documentclass{article}
% ateb: https://tex.stackexchange.com/a/700683/  i gwestiwn Bernhard: https://tex.stackexchange.com/q/700671/
\usepackage{fitch}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\usetikzlibrary{fit}
\usetikzlibrary{calc}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}[remember picture]
  \node [align=center] {%
    $\begin{nd}
      \hypo {1} {P \lor Q} \by{}{}%
      \hypo {2} {P \rightarrow R} \by{}{}%
      \hypo {3} {Q\tikzmark{e} \rightarrow R} \by{}{}%
      \open 
      \hypo {4} {\subnode{f}{P}} \by{}{}
      \have {5} {\subnode{g}{R}} \by{\subnode{h}{\strut}}{}
      \close
      \open
      \hypo {6} {Q} \by{}{}%
      \have {7} {R} \by{}{}%
      \close
      \have {8} {R} \by{}{}%
    \end{nd}$
  };
  \scoped[on background layer]
  {
    \node [fit=({pic cs:e} |- f) (f) (g) ($(h.south)!.75!(g |- h.south)$),fill=cyan!25] {};
  }
\end{tikzpicture}
\end{document}