diff -r bda7527ccf05 -r cc2d676d5395 src/Doc/Tutorial/CTL/CTLind.thy --- a/src/Doc/Tutorial/CTL/CTLind.thy Wed Dec 26 16:07:28 2018 +0100 +++ b/src/Doc/Tutorial/CTL/CTLind.thy Wed Dec 26 16:25:20 2018 +0100 @@ -10,7 +10,7 @@ In \S\ref{sec:CTL} we gave a fairly involved proof of the correctness of a model checker for CTL\@. In particular the proof of the @{thm[source]infinity_lemma} on the way to @{thm[source]AF_lemma2} is not as -simple as one might expect, due to the @{text SOME} operator +simple as one might expect, due to the \SOME\ operator involved. Below we give a simpler proof of @{thm[source]AF_lemma2} based on an auxiliary inductive definition. @@ -39,7 +39,7 @@ The proof is by induction on @{prop"f(0::nat) \ Avoid s A"}. However, this requires the following reformulation, as explained in \S\ref{sec:ind-var-in-prems} above; -the @{text rule_format} directive undoes the reformulation after the proof. +the \rule_format\ directive undoes the reformulation after the proof. \ lemma ex_infinite_path[rule_format]: @@ -53,10 +53,10 @@ done text\\noindent -The base case (@{prop"t = s"}) is trivial and proved by @{text blast}. +The base case (@{prop"t = s"}) is trivial and proved by \blast\. In the induction step, we have an infinite @{term A}-avoiding path @{term f} starting from @{term u}, a successor of @{term t}. Now we simply instantiate -the @{text"\f\Paths t"} in the induction hypothesis by the path starting with +the \\f\Paths t\ in the induction hypothesis by the path starting with @{term t} and continuing with @{term f}. That is what the above $\lambda$-term expresses. Simplification shows that this is a path starting with @{term t} and that the instantiated induction hypothesis implies the conclusion. @@ -129,11 +129,11 @@ done text\ -The @{text"(no_asm)"} modifier of the @{text"rule_format"} directive in the +The \(no_asm)\ modifier of the \rule_format\ directive in the statement of the lemma means -that the assumption is left unchanged; otherwise the @{text"\p"} +that the assumption is left unchanged; otherwise the \\p\ would be turned -into a @{text"\p"}, which would complicate matters below. As it is, +into a \\p\, which would complicate matters below. As it is, @{thm[source]Avoid_in_lfp} is now @{thm[display]Avoid_in_lfp[no_vars]} The main theorem is simply the corollary where @{prop"t = s"},