diff -r ea69ee7e117b -r 2d4c058749a7 doc-src/TutorialI/CTL/PDL.thy --- a/doc-src/TutorialI/CTL/PDL.thy Sat Jan 06 10:36:19 2001 +0100 +++ b/doc-src/TutorialI/CTL/PDL.thy Sat Jan 06 11:27:09 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^-1 ^^ T)" +"mc(EF f) = lfp(\T. mc f \ M^-1 ``` T)" text{*\noindent Only the equation for @{term EF} deserves some comments. Remember that the -postfix @{text"^-1"} and the infix @{text"^^"} are predefined and denote the +postfix @{text"^-1"} 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^-1 ^^ T"} is the set of all predecessors of @{term T} and the least -fixed point (@{term lfp}) of @{term"\T. mc f \ M^-1 ^^ T"} is the least set +@{term "M^-1 ``` T"} is the set of all predecessors of @{term T} and the least +fixed point (@{term lfp}) of @{term"\T. mc f \ M^-1 ``` 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^-1 ^^ T)" +lemma mono_ef: "mono(\T. A \ M^-1 ``` T)" apply(rule monoI) apply blast done @@ -87,7 +87,7 @@ *} lemma EF_lemma: - "lfp(\T. A \ M^-1 ^^ T) = {s. \t. (s,t) \ M^* \ t \ A}" + "lfp(\T. A \ M^-1 ``` T) = {s. \t. (s,t) \ M^* \ t \ A}" txt{*\noindent The equality is proved in the canonical fashion by proving that each set