src/HOL/HOLCF/IOA/NTP/Sender.thy
changeset 67613 ce654b0e6d69
parent 66453 cc19f7ca2ed6
--- a/src/HOL/HOLCF/IOA/NTP/Sender.thy	Tue Feb 13 14:24:50 2018 +0100
+++ b/src/HOL/HOLCF/IOA/NTP/Sender.thy	Thu Feb 15 12:11:00 2018 +0100
@@ -31,41 +31,41 @@
           t = snd(snd(tr))
       in case fst(snd(tr))
       of
-      S_msg(m) => sq(t)=sq(s)@[m]   &
-                  ssent(t)=ssent(s) &
-                  srcvd(t)=srcvd(s) &
-                  sbit(t)=sbit(s)   &
+      S_msg(m) => sq(t)=sq(s)@[m]   \<and>
+                  ssent(t)=ssent(s) \<and>
+                  srcvd(t)=srcvd(s) \<and>
+                  sbit(t)=sbit(s)   \<and>
                   ssending(t)=ssending(s) |
       R_msg(m) => False |
-      S_pkt(pkt) => hdr(pkt) = sbit(s)      &
-                       (? Q. sq(s) = (msg(pkt)#Q))  &
-                       sq(t) = sq(s)           &
-                       ssent(t) = addm (ssent s) (sbit s) &
-                       srcvd(t) = srcvd(s) &
-                       sbit(t) = sbit(s)   &
-                       ssending(s)         &
+      S_pkt(pkt) => hdr(pkt) = sbit(s)      \<and>
+                       (\<exists>Q. sq(s) = (msg(pkt)#Q))  \<and>
+                       sq(t) = sq(s)           \<and>
+                       ssent(t) = addm (ssent s) (sbit s) \<and>
+                       srcvd(t) = srcvd(s) \<and>
+                       sbit(t) = sbit(s)   \<and>
+                       ssending(s)         \<and>
                        ssending(t) |
     R_pkt(pkt) => False |
     S_ack(b)   => False |
-      R_ack(b) => sq(t)=sq(s)                  &
-                     ssent(t)=ssent(s)            &
-                     srcvd(t) = addm (srcvd s) b  &
-                     sbit(t)=sbit(s)              &
+      R_ack(b) => sq(t)=sq(s)                  \<and>
+                     ssent(t)=ssent(s)            \<and>
+                     srcvd(t) = addm (srcvd s) b  \<and>
+                     sbit(t)=sbit(s)              \<and>
                      ssending(t)=ssending(s) |
-      C_m_s => count (ssent s) (~sbit s) < count (srcvd s) (~sbit s) &
-               sq(t)=sq(s)       &
-               ssent(t)=ssent(s) &
-               srcvd(t)=srcvd(s) &
-               sbit(t)=sbit(s)   &
-               ssending(s)       &
+      C_m_s => count (ssent s) (~sbit s) < count (srcvd s) (~sbit s) \<and>
+               sq(t)=sq(s)       \<and>
+               ssent(t)=ssent(s) \<and>
+               srcvd(t)=srcvd(s) \<and>
+               sbit(t)=sbit(s)   \<and>
+               ssending(s)       \<and>
                ~ssending(t) |
       C_m_r => False |
-      C_r_s => count (ssent s) (sbit s) <= count (srcvd s) (~sbit s) &
-               sq(t)=tl(sq(s))      &
-               ssent(t)=ssent(s)    &
-               srcvd(t)=srcvd(s)    &
-               sbit(t) = (~sbit(s)) &
-               ~ssending(s)         &
+      C_r_s => count (ssent s) (sbit s) <= count (srcvd s) (~sbit s) \<and>
+               sq(t)=tl(sq(s))      \<and>
+               ssent(t)=ssent(s)    \<and>
+               srcvd(t)=srcvd(s)    \<and>
+               sbit(t) = (~sbit(s)) \<and>
+               ~ssending(s)         \<and>
                ssending(t) |
       C_r_r(m) => False}"
 
@@ -74,17 +74,17 @@
   "sender_ioa =
    (sender_asig, {([],{|},{|},False,True)}, sender_trans,{},{})"
 
-lemma in_sender_asig: 
-  "S_msg(m) : actions(sender_asig)"
-  "R_msg(m) ~: actions(sender_asig)"
-  "S_pkt(pkt) : actions(sender_asig)"
-  "R_pkt(pkt) ~: actions(sender_asig)"
-  "S_ack(b) ~: actions(sender_asig)"
-  "R_ack(b) : actions(sender_asig)"
-  "C_m_s : actions(sender_asig)"
-  "C_m_r ~: actions(sender_asig)"
-  "C_r_s : actions(sender_asig)"
-  "C_r_r(m) ~: actions(sender_asig)"
+lemma in_sender_asig:
+  "S_msg(m) \<in> actions(sender_asig)"
+  "R_msg(m) \<notin> actions(sender_asig)"
+  "S_pkt(pkt) \<in> actions(sender_asig)"
+  "R_pkt(pkt) \<notin> actions(sender_asig)"
+  "S_ack(b) \<notin> actions(sender_asig)"
+  "R_ack(b) \<in> actions(sender_asig)"
+  "C_m_s \<in> actions(sender_asig)"
+  "C_m_r \<notin> actions(sender_asig)"
+  "C_r_s \<in> actions(sender_asig)"
+  "C_r_r(m) \<notin> actions(sender_asig)"
   by (simp_all add: sender_asig_def actions_def asig_projections)
 
 lemmas sender_projections = sq_def ssent_def srcvd_def sbit_def ssending_def