equal
deleted
inserted
replaced
126 into a @{text"\<And>p"}, which would complicate matters below. As it is, |
126 into a @{text"\<And>p"}, which would complicate matters below. As it is, |
127 @{thm[source]Avoid_in_lfp} is now |
127 @{thm[source]Avoid_in_lfp} is now |
128 @{thm[display]Avoid_in_lfp[no_vars]} |
128 @{thm[display]Avoid_in_lfp[no_vars]} |
129 The main theorem is simply the corollary where @{prop"t = s"}, |
129 The main theorem is simply the corollary where @{prop"t = s"}, |
130 in which case the assumption @{prop"t \<in> Avoid s A"} is trivially true |
130 in which case the assumption @{prop"t \<in> Avoid s A"} is trivially true |
131 by the first @{term Avoid}-rule). Isabelle confirms this: |
131 by the first @{term Avoid}-rule. Isabelle confirms this: |
132 *} |
132 *} |
133 |
133 |
134 theorem AF_lemma2: |
134 theorem AF_lemma2: |
135 "{s. \<forall>p \<in> Paths s. \<exists> i. p i \<in> A} \<subseteq> lfp(af A)"; |
135 "{s. \<forall>p \<in> Paths s. \<exists> i. p i \<in> A} \<subseteq> lfp(af A)"; |
136 by(auto elim:Avoid_in_lfp intro:Avoid.intros); |
136 by(auto elim:Avoid_in_lfp intro:Avoid.intros); |