diff -r 9423817dee84 -r 1f93f5a27de6 doc-src/TutorialI/CTL/PDL.thy --- a/doc-src/TutorialI/CTL/PDL.thy Wed Jan 10 00:15:33 2001 +0100 +++ b/doc-src/TutorialI/CTL/PDL.thy Wed Jan 10 10:40:34 2001 +0100 @@ -58,14 +58,14 @@ "mc(Neg f) = -mc f" "mc(And f g) = mc f \ mc g" "mc(AX f) = {s. \t. (s,t) \ M \ t \ mc f}" -"mc(EF f) = lfp(\T. mc f \ M\ ``` T)" +"mc(EF f) = lfp(\T. mc f \ M\ `` T)" text{*\noindent Only the equation for @{term EF} deserves some comments. Remember that the -postfix @{text"\"} and the infix @{text"```"} are predefined and denote the +postfix @{text"\"} and the infix @{text"``"} are predefined and denote the converse of a relation and the application of a relation to a set. Thus -@{term "M\ ``` T"} is the set of all predecessors of @{term T} and the least -fixed point (@{term lfp}) of @{term"\T. mc f \ M\ ``` T"} is the least set +@{term "M\ `` T"} is the set of all predecessors of @{term T} and the least +fixed point (@{term lfp}) of @{term"\T. mc f \ M\ `` T"} is the least set @{term T} containing @{term"mc f"} and all predecessors of @{term T}. If you find it hard to see that @{term"mc(EF f)"} contains exactly those states from which there is a path to a state where @{term f} is true, do not worry---that @@ -74,7 +74,7 @@ First we prove monotonicity of the function inside @{term lfp} *} -lemma mono_ef: "mono(\T. A \ M\ ``` T)" +lemma mono_ef: "mono(\T. A \ M\ `` T)" apply(rule monoI) apply blast done @@ -87,7 +87,7 @@ *} lemma EF_lemma: - "lfp(\T. A \ M\ ``` T) = {s. \t. (s,t) \ M\<^sup>* \ t \ A}" + "lfp(\T. A \ M\ `` T) = {s. \t. (s,t) \ M\<^sup>* \ t \ A}" txt{*\noindent The equality is proved in the canonical fashion by proving that each set