--- a/src/HOLCF/IOA/meta_theory/Traces.ML Mon Jun 22 17:12:27 1998 +0200
+++ b/src/HOLCF/IOA/meta_theory/Traces.ML Mon Jun 22 17:13:09 1998 +0200
@@ -26,15 +26,15 @@
(* ---------------------------------------------------------------- *)
-goal thy "filter_act`UU = UU";
+Goal "filter_act`UU = UU";
by (simp_tac (simpset() addsimps [filter_act_def]) 1);
qed"filter_act_UU";
-goal thy "filter_act`nil = nil";
+Goal "filter_act`nil = nil";
by (simp_tac (simpset() addsimps [filter_act_def]) 1);
qed"filter_act_nil";
-goal thy "filter_act`(x>>xs) = (fst x) >> filter_act`xs";
+Goal "filter_act`(x>>xs) = (fst x) >> filter_act`xs";
by (simp_tac (simpset() addsimps [filter_act_def]) 1);
qed"filter_act_cons";
@@ -45,15 +45,15 @@
(* mk_trace *)
(* ---------------------------------------------------------------- *)
-goal thy "mk_trace A`UU=UU";
+Goal "mk_trace A`UU=UU";
by (simp_tac (simpset() addsimps [mk_trace_def]) 1);
qed"mk_trace_UU";
-goal thy "mk_trace A`nil=nil";
+Goal "mk_trace A`nil=nil";
by (simp_tac (simpset() addsimps [mk_trace_def]) 1);
qed"mk_trace_nil";
-goal thy "mk_trace A`(at >> xs) = \
+Goal "mk_trace A`(at >> xs) = \
\ (if ((fst at):ext A) \
\ then (fst at) >> (mk_trace A`xs) \
\ else mk_trace A`xs)";
@@ -68,7 +68,7 @@
(* ---------------------------------------------------------------- *)
-goal thy "is_exec_fragC A = (LAM ex. (%s. case ex of \
+Goal "is_exec_fragC A = (LAM ex. (%s. case ex of \
\ nil => TT \
\ | x##xs => (flift1 \
\ (%p. Def ((s,p):trans_of A) andalso (is_exec_fragC A`xs) (snd p)) \
@@ -81,17 +81,17 @@
by (simp_tac (simpset() addsimps [flift1_def]) 1);
qed"is_exec_fragC_unfold";
-goal thy "(is_exec_fragC A`UU) s=UU";
+Goal "(is_exec_fragC A`UU) s=UU";
by (stac is_exec_fragC_unfold 1);
by (Simp_tac 1);
qed"is_exec_fragC_UU";
-goal thy "(is_exec_fragC A`nil) s = TT";
+Goal "(is_exec_fragC A`nil) s = TT";
by (stac is_exec_fragC_unfold 1);
by (Simp_tac 1);
qed"is_exec_fragC_nil";
-goal thy "(is_exec_fragC A`(pr>>xs)) s = \
+Goal "(is_exec_fragC A`(pr>>xs)) s = \
\ (Def ((s,pr):trans_of A) \
\ andalso (is_exec_fragC A`xs)(snd pr))";
by (rtac trans 1);
@@ -108,15 +108,15 @@
(* is_exec_frag *)
(* ---------------------------------------------------------------- *)
-goal thy "is_exec_frag A (s, UU)";
+Goal "is_exec_frag A (s, UU)";
by (simp_tac (simpset() addsimps [is_exec_frag_def]) 1);
qed"is_exec_frag_UU";
-goal thy "is_exec_frag A (s, nil)";
+Goal "is_exec_frag A (s, nil)";
by (simp_tac (simpset() addsimps [is_exec_frag_def]) 1);
qed"is_exec_frag_nil";
-goal thy "is_exec_frag A (s, (a,t)>>ex) = \
+Goal "is_exec_frag A (s, (a,t)>>ex) = \
\ (((s,a,t):trans_of A) & \
\ is_exec_frag A (t, ex))";
by (simp_tac (simpset() addsimps [is_exec_frag_def]) 1);
@@ -130,15 +130,15 @@
section "laststate";
(* ---------------------------------------------------------------------------- *)
-goal thy "laststate (s,UU) = s";
+Goal "laststate (s,UU) = s";
by (simp_tac (simpset() addsimps [laststate_def]) 1);
qed"laststate_UU";
-goal thy "laststate (s,nil) = s";
+Goal "laststate (s,nil) = s";
by (simp_tac (simpset() addsimps [laststate_def]) 1);
qed"laststate_nil";
-goal thy "!! ex. Finite ex ==> laststate (s,at>>ex) = laststate (snd at,ex)";
+Goal "!! ex. Finite ex ==> laststate (s,at>>ex) = laststate (snd at,ex)";
by (simp_tac (simpset() addsimps [laststate_def]) 1);
by (case_tac "ex=nil" 1);
by (Asm_simp_tac 1);
@@ -150,7 +150,7 @@
Addsimps [laststate_UU,laststate_nil,laststate_cons];
-goal thy "!!ex. Finite ex ==> (! s. ? u. laststate (s,ex)=u)";
+Goal "!!ex. Finite ex ==> (! s. ? u. laststate (s,ex)=u)";
by (Seq_Finite_induct_tac 1);
qed"exists_laststate";
@@ -162,7 +162,7 @@
(* alternative definition of has_trace tailored for the refinement proof, as it does not
take the detour of schedules *)
-goalw thy [executions_def,mk_trace_def,has_trace_def,schedules_def,has_schedule_def]
+Goalw [executions_def,mk_trace_def,has_trace_def,schedules_def,has_schedule_def]
"has_trace A b = (? ex:executions A. b = mk_trace A`(snd ex))";
by (safe_tac set_cs);
@@ -193,7 +193,7 @@
For executions of parallel automata this assumption is not needed, as in par_def
this condition is included once more. (see Lemmas 1.1.1c in CompoExecs for example) *)
-goal thy
+Goal
"!! A. is_trans_of A ==> \
\ ! s. is_exec_frag A (s,xs) --> Forall (%a. a:act A) (filter_act`xs)";
@@ -204,7 +204,7 @@
by (REPEAT (asm_full_simp_tac (simpset() addsimps [is_trans_of_def]) 1));
qed"execfrag_in_sig";
-goal thy
+Goal
"!! A.[| is_trans_of A; x:executions A |] ==> \
\ Forall (%a. a:act A) (filter_act`(snd x))";
@@ -214,7 +214,7 @@
by Auto_tac;
qed"exec_in_sig";
-goalw thy [schedules_def,has_schedule_def]
+Goalw [schedules_def,has_schedule_def]
"!! A.[| is_trans_of A; x:schedules A |] ==> \
\ Forall (%a. a:act A) x";
@@ -225,7 +225,7 @@
is ok but needs ForallQFilterP which has to been proven first (is trivial also)
-goalw thy [traces_def,has_trace_def]
+Goalw [traces_def,has_trace_def]
"!! A.[| x:traces A |] ==> \
\ Forall (%a. a:act A) x";
by (safe_tac set_cs );
@@ -240,7 +240,7 @@
section "executions are prefix closed";
(* only admissible in y, not if done in x !! *)
-goal thy "!x s. is_exec_frag A (s,x) & y<<x --> is_exec_frag A (s,y)";
+Goal "!x s. is_exec_frag A (s,x) & y<<x --> is_exec_frag A (s,y)";
by (pair_induct_tac "y" [is_exec_frag_def] 1);
by (strip_tac 1);
by (Seq_case_simp_tac "xa" 1);
@@ -253,7 +253,7 @@
(* second prefix notion for Finite x *)
-goal thy "! y s. is_exec_frag A (s,x@@y) --> is_exec_frag A (s,x)";
+Goal "! y s. is_exec_frag A (s,x@@y) --> is_exec_frag A (s,x)";
by (pair_induct_tac "x" [is_exec_frag_def] 1);
by (strip_tac 1);
by (Seq_case_simp_tac "s" 1);