In a recent research paper, I formalised some of my theorems in the proof assistant Isabelle, but left some of them as just proved ‘by hand’. I found it helpful to use a different ‘QED’ symbol depending on which method I had used.
Below is an enlarged version of the ‘three cubes’ symbol in the snippet above, together with the original Isabelle logo for comparison. The new symbol is designed to be suitable for black-and-white printing at a small size, and can be generated by the LaTeX code given below.
\usepackage{tikz}
\newcommand{\isabelleqed}{%
\begin{tikzpicture}[x=0.8mm, y=0.8mm,
baseline=-0.3mm, line join=round]
\begin{scope}[yslant=-0.5]
\draw (0,0) rectangle +(1,1);
\draw (2,1) rectangle +(1,1);
\draw (1,2) rectangle +(1,1);
\end{scope}
\begin{scope}[yslant=0.5]
\filldraw (1,-1) rectangle +(1,1);
\filldraw (3,-2) rectangle +(1,1);
\filldraw (2,0) rectangle +(1,1);
\end{scope}
\begin{scope}[yslant=0.5,xslant=-1]
\draw (1,0) rectangle +(1,1);
\draw (2,-1) rectangle +(1,1);
\draw (3,1) rectangle +(1,1);
\end{scope}
\end{tikzpicture}%
}
One could even go a step further, and extend this idea into a potential new logo for Isabelle.
The picture above is generated by the following LaTeX code.
\begin{tikzpicture}[x=4mm, y=4mm, baseline=6mm,
line join=round, draw=black]
\begin{scope}[every node/.append style={yslant=-0.5}, yslant=-0.5]
\filldraw[fill=blue!25] (0,0) rectangle +(1,1);
\node at (0.5,0.5) {$\lambda$};
\filldraw[fill=blue!25] (2,1) rectangle +(1,1);
\node at (2.5,1.5) {$=$};
\filldraw[fill=yellow!25] (1,2) rectangle +(1,1);
\node at (1.5,2.5) {$\vdash$};
\filldraw[fill=red!25] (4,2) rectangle +(1,1);
\node at (4.5,2.5) {$\alpha$};
\filldraw[fill=red!25] (3,3) rectangle +(1,1);
\node at (3.5,3.5) {$\rightarrow$};
\filldraw[fill=yellow!25] (2,4) rectangle +(1,1);
\node at (2.5,4.5) {$\forall$};
\end{scope}
\begin{scope}[yslant=0.5]
\filldraw[fill=black!25!blue] (1,-1) rectangle +(1,1);
\filldraw[fill=black!25!blue] (3,-2) rectangle +(1,1);
\filldraw[fill=black!25!yellow] (2,0) rectangle +(1,1);
\filldraw[fill=black!25!yellow] (3,1) rectangle +(1,1);
\filldraw[fill=black!25!red] (4,-1) rectangle +(1,1);
\filldraw[fill=black!25!red] (5,-3) rectangle +(1,1);
\end{scope}
\begin{scope}[yslant=0.5,xslant=-1]
\filldraw[fill=blue] (1,0) rectangle +(1,1);
\filldraw[fill=blue] (2,-1) rectangle +(1,1);
\filldraw[fill=yellow] (3,1) rectangle +(1,1);
\filldraw[fill=yellow] (5,2) rectangle +(1,1);
\filldraw[fill=red] (4,0) rectangle +(1,1);
\filldraw[fill=red] (3,-2) rectangle +(1,1);
\end{scope}
\end{tikzpicture}\hspace{4mm}{\Huge\bf Isabelle}
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