ex/Simult.ML

--- a/ex/Simult.ML	Thu Aug 18 12:42:19 1994 +0200
+++ b/ex/Simult.ML	Thu Aug 18 12:48:03 1994 +0200
@@ -1,9 +1,9 @@
-(*  Title: 	HOL/ex/simult.ML
+(*  Title: 	HOL/ex/Simult.ML
     ID:         $Id$
     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1993  University of Cambridge
 
-For simult.thy.
+For Simult.thy.
 
 Primitives for simultaneous recursive type definitions
   includes worked example of trees & forests
@@ -15,30 +15,6 @@
 
 open Simult;
 
-(*** General rules for Part ***)
-
-val prems = goalw Simult.thy [Part_def] "h(a) : A ==> h(a) : Part(A,h)";
-by (cfast_tac prems 1);
-val PartI = result();
-
-val major::prems = goalw Simult.thy [Part_def]
-    "[| a : Part(A,h);  !!z. [| a : A;  a=h(z) |] ==> P  \
-\    |] ==> P";
-by (rtac (major RS CollectE) 1);
-by (etac conjE 1);
-by (etac exE 1);
-by (REPEAT (ares_tac prems 1));
-val PartE = result();
-
-goal Simult.thy "!!A B. A<=B ==> Part(A,h) <= Part(B,h)";
-by (fast_tac (set_cs addSIs [PartI] addSEs [PartE]) 1);
-val Part_mono = result();
-
-val [prem] = goal Simult.thy "A<=B ==> Part(A,h) <= B";
-by (fast_tac (set_cs addSIs [PartI, prem RS subsetD] addSEs [PartE]) 1);
-val Part_subset = result();
-
-
 (*** Monotonicity and unfolding of the function ***)
 
 goal Simult.thy "mono(%Z.  A <*> Part(Z,In1) \
@@ -259,48 +235,43 @@
 
 (** conversion rules for TF_rec **)
 
-val prems = goalw Simult.thy [TCONS_def]
-    "[| M: Sexp;  N: Sexp |] ==> 	\
-\    TF_rec(TCONS(M,N),b,c,d) = b(M, N, TF_rec(N,b,c,d))";
+goalw Simult.thy [TCONS_def]
+    "!!M N. [| M: Sexp;  N: Sexp |] ==> 	\
+\           TF_rec(TCONS(M,N),b,c,d) = b(M, N, TF_rec(N,b,c,d))";
 by (rtac (TF_rec_unfold RS trans) 1);
-by (rtac (Case_In0 RS trans) 1);
-by (rtac (Split RS trans) 1);
-by (rewtac In0_def);
-by (simp_tac (pred_Sexp_ss addsimps prems) 1);
+by (simp_tac (HOL_ss addsimps [Case_In0, Split]) 1);
+by (asm_simp_tac (pred_Sexp_ss addsimps [In0_def]) 1);
 val TF_rec_TCONS = result();
 
 goalw Simult.thy [FNIL_def] "TF_rec(FNIL,b,c,d) = c";
 by (rtac (TF_rec_unfold RS trans) 1);
-by (rtac (Case_In1 RS trans) 1);
-by (rtac List_case_NIL 1);
+by (simp_tac (HOL_ss addsimps [Case_In1, List_case_NIL]) 1);
 val TF_rec_FNIL = result();
 
-val prems = goalw Simult.thy [FCONS_def]
-    "[| M: Sexp;  N: Sexp |] ==> 	\
-\    TF_rec(FCONS(M,N),b,c,d) = d(M, N, TF_rec(M,b,c,d), TF_rec(N,b,c,d))";
+goalw Simult.thy [FCONS_def]
+ "!!M N. [| M: Sexp;  N: Sexp |] ==> 	\
+\        TF_rec(FCONS(M,N),b,c,d) = d(M, N, TF_rec(M,b,c,d), TF_rec(N,b,c,d))";
 by (rtac (TF_rec_unfold RS trans) 1);
-by (rtac (Case_In1 RS trans) 1);
-by (rtac (List_case_CONS RS trans) 1);
-by (rewrite_goals_tac [CONS_def,In1_def]);
-by (simp_tac (pred_Sexp_ss addsimps prems) 1);
+by (simp_tac (HOL_ss addsimps [Case_In1, List_case_CONS]) 1);
+by (asm_simp_tac (pred_Sexp_ss addsimps [CONS_def,In1_def]) 1);
 val TF_rec_FCONS = result();
 
 
 (*** tree_rec, forest_rec -- by TF_rec ***)
 
 val Rep_Tree_in_Sexp =
-    Rep_Tree RS (range_Leaf_subset_Sexp RS TF_subset_Sexp RS 
-		   Part_subset RS subsetD);
+    [range_Leaf_subset_Sexp RS TF_subset_Sexp RS (Part_subset RS subset_trans),
+     Rep_Tree] MRS subsetD;
 val Rep_Forest_in_Sexp =
-    Rep_Forest RS (range_Leaf_subset_Sexp RS TF_subset_Sexp RS 
-		   Part_subset RS subsetD);
+    [range_Leaf_subset_Sexp RS TF_subset_Sexp RS (Part_subset RS subset_trans),
+     Rep_Forest] MRS subsetD;
 
 val tf_rec_simps = [TF_rec_TCONS, TF_rec_FNIL, TF_rec_FCONS,
-		 TCONS_I, FNIL_I, FCONS_I, Rep_Tree, Rep_Forest,
-		 Rep_Tree_inverse, Rep_Forest_inverse,
-		 Abs_Tree_inverse, Abs_Forest_inverse,
-		 inj_Leaf, Inv_f_f, Sexp_LeafI, range_eqI,
-		 Rep_Tree_in_Sexp, Rep_Forest_in_Sexp];
+		    TCONS_I, FNIL_I, FCONS_I, Rep_Tree, Rep_Forest,
+		    Rep_Tree_inverse, Rep_Forest_inverse,
+		    Abs_Tree_inverse, Abs_Forest_inverse,
+		    inj_Leaf, Inv_f_f, Sexp_LeafI, range_eqI,
+		    Rep_Tree_in_Sexp, Rep_Forest_in_Sexp];
 val tf_rec_ss = HOL_ss addsimps tf_rec_simps;
 
 goalw Simult.thy [tree_rec_def, forest_rec_def, Tcons_def]