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

@@ -11,16 +11,16 @@ 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
+	the semantics of the proof format was added.
+	\item A description of the semantics 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
+   $(f\;x\;(g\;y))$).  This is 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
+  \item There 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.
@@ -30,7 +30,7 @@ Proof rules:
 \begin{itemize}
   \item The rule \proofRule{implies_simplify} is no longer allowed to
   perform the simplification $(\varphi_1\rightarrow \varphi_2)\rightarrow \varphi_2
-  ⇒  \varphi_1\lor \varphi_2$.  This is covered by \proofRule{bool_simplify}.
+  ⇒  \varphi_1\lor \varphi_2$.  This is now covered by \proofRule{bool_simplify}.
 \end{itemize}
 
 \subsection*{0.2 --- \DTMdisplaydate{2022}{12}{19}{-1}}