
diff -r e67eed4cd224 -r bb282845ca77 doc-src/IsarRef/pure.tex
--- a/doc-src/IsarRef/pure.tex	Fri Sep 03 16:11:03 1999 +0200
+++ b/doc-src/IsarRef/pure.tex	Fri Sep 03 16:11:53 1999 +0200
@@ -410,8 +410,8 @@
 \item [$proof(state)$] is like an internal theory mode: the context may be
   augmented by \emph{stating} additional assumptions, intermediate result etc.
 \item [$proof(chain)$] is an intermediate mode between $proof(state)$ and
-  $proof(prove)$: existing facts have been just picked up in order to use them
-  when refining the goal claimed next.
+  $proof(prove)$: existing facts (i.e.\ the contents of $this$) have been just
+  picked up in order to use them when refining the goal claimed next.
 \end{descr}
 
 
@@ -478,7 +478,7 @@
 
   var: name ('::' type)?
   ;
-  vars: name+ ('::' type)?
+  vars: (name+) ('::' type)?
   ;
   assm: thmdecl? (prop proppat? +)
   ;
@@ -521,7 +521,7 @@
 Any fact will usually be involved in further proofs, either as explicit
 arguments of proof methods or when forward chaining towards the next goal via
 $\THEN$ (and variants).  Note that the special theorem name
-$facts$.\indexisarthm{facts} refers to the most recently established facts.
+$this$.\indexisarthm{this} refers to the most recently established facts.
 \begin{rail}
   'note' thmdef? thmrefs comment?
   ;
@@ -541,7 +541,7 @@
   \S\ref{sec:proof-steps}).  For example, method $rule$ (see
   \S\ref{sec:pure-meth}) would do an elimination rather than an introduction.
 \item [$\FROM{\vec b}$] abbreviates $\NOTE{}{\vec b}~\THEN$; thus $\THEN$ is
-  equivalent to $\FROM{facts}$.
+  equivalent to $\FROM{this}$.
 \item [$\WITH{\vec b}$] abbreviates $\FROM{\vec b~facts}$; thus the forward
   chaining is from earlier facts together with the current ones.
 \end{descr}
@@ -549,9 +549,9 @@
 Basic proof methods (such as $rule$, see \S\ref{sec:pure-meth}) expect
 multiple facts to be given in proper order, corresponding to a prefix of the
 premises of the rule involved.  Note that positions may be easily skipped
-using a form like $\FROM{_~a~b}$, for example.  This involves the rule
-$PROP~\psi \Imp PROP~\psi$, which is bound in Isabelle/Pure as ``_''
-(underscore).\indexisarthm{_@\texttt{_}}
+using a form like $\FROM{\text{\texttt{_}}~a~b}$, for example.  This involves
+the rule $\PROP\psi \Imp \PROP\psi$, which is bound in Isabelle/Pure as
+``\texttt{_}'' (underscore).\indexisarthm{_@\texttt{_}}
 
 
 \subsection{Goal statements}
@@ -593,8 +593,10 @@
 \item [$\SHOW{a}{\phi}$] is similar to $\HAVE{a}{\phi}$, but solves some
   pending goal with the result \emph{exported} into the corresponding context.
 \item [$\HENCE{a}{\phi}$] abbreviates $\THEN~\HAVE{a}{\phi}$, i.e.\ claims a
-  local goal to be proven by forward chaining the current facts.
-\item [$\THUS{a}{\phi}$] abbreviates $\THEN~\SHOW{a}{\phi}$.
+  local goal to be proven by forward chaining the current facts.  Note that
+  $\HENCENAME$ is equivalent to $\FROM{this}~\HAVENAME$.
+\item [$\THUS{a}{\phi}$] abbreviates $\THEN~\SHOW{a}{\phi}$.  Note that
+  $\THUSNAME$ is equivalent to $\FROM{this}~\SHOWNAME$.
 \end{descr}
 
 
@@ -639,8 +641,9 @@
 
 Unless given explicitly by the user, the default initial method is
 ``$default$'', which is usually set up to apply a single standard elimination
-or introduction rule according to the topmost symbol involved.  The default
-terminal method is ``$finish$''; it solves all goals by assumption.
+or introduction rule according to the topmost symbol involved.  There is no
+default terminal method; in any case the final step is to solve all remaining
+goals by assumption.
 
 \begin{rail}
   'proof' interest? meth? comment?
@@ -673,7 +676,8 @@
   expanding the abbreviation by hand; note that $\PROOF{m@1}$ is usually
   sufficient to see what is going wrong.
 \item [``$\DDOT$''] is a \emph{default proof}; it abbreviates $\BY{default}$.
-\item [``$\DOT$''] is a \emph{trivial proof}; it abbreviates $\BY{-}$.
+\item [``$\DOT$''] is a \emph{trivial proof}; it abbreviates
+  $\BY{assumption}$.
 \item [$\isarkeyword{sorry}$] is a \emph{fake proof}; provided that
   \texttt{quick_and_dirty} is enabled, $\isarkeyword{sorry}$ pretends to solve
   the goal without further ado.  Of course, the result is a fake theorem only,
@@ -734,7 +738,7 @@
 higher-order matching is applied to bind extra-logical text
 variables\index{text variables}, which may be either of the form $\VVar{x}$
 (token class \railtoken{textvar}, see \S\ref{sec:lex-syntax}) or nameless
-dummies ``\verb,_,'' (underscore).\index{dummy variables} Note that in the
+dummies ``\texttt{_}'' (underscore).\index{dummy variables} Note that in the
 $\LETNAME$ form the patterns occur on the left-hand side, while the $\ISNAME$
 patterns are in postfix position.
 




