Backport specification from my PhD thesis

This replaces the text of the specification and the rule list with the text in my PhD thesis.

Most importantly this adds an abstract proof checking procedure that specifies the semantic of an Altehe proof (modulo the proof rules).

Furthermore, it adapts the notation more to SMT-LIB: everything is in λ-application style ((f x) instead of f(x)) and we no longer have a distinct connective. Instead we use the equality predicate everywhere.

On the technical side this now requires lualatex for Unicode math.

spec/changelog.tex

+\subsection*{0.3 --- Unreleased}
+
+This release overhauls the entire document, but introduces only few
+changes to the proof format itself.
+
+The standard now specifies that \texttt{assume} commands can only be
+issued at the start of the proof or right after an \texttt{anchor}
+command.
+
+Beyond many smaller clarifications and typographic improvments, the
+following changes were implemented in this release.
+\begin{itemize}
+	\item An abstract proof checking procedure to clarify
+	the semantic of the proof format was added.
+	\item A description of the semantic of contexts based on λ-terms
+	was added.
+  \item The document now lists all transformations that are
+  implicit in Alethe proofs.
+  \item The notation used for terms from first-order style
+   (e.g., $f(x,g(y))$) was changed to higher-order style (e.g.,
+   $(f\;x\;(g\;y))$).  This only a change in notation -- the used logic
+   remains many-sorted first-order logic.
+  \item The is no longer a distinction between if-and-only-if and
+   equaltiy.  Instead equality (the symbol $≈$) is used with appropiate
+   sorts.
+  \item An index that lists all proof rules was added.
+\end{itemize}
+
 \subsection*{0.2 --- \DTMdisplaydate{2022}{12}{19}{-1}}
 
 This is an intermediate release.  It collects all changes to the original