src/HOL/Imperative_HOL/ex/Imperative_Reverse.thy

 *)
 
 header {* An imperative in-place reversal on arrays *}
 
 theory Imperative_Reverse
-imports "~~/src/HOL/Imperative_HOL/Imperative_HOL" Subarray
+imports Imperative_HOL Subarray
 begin
 
 hide_const (open) swap rev
 
 fun swap :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap" where

 lemma swap_pointwise: assumes "crel (swap a i j) h h' r"
   shows "get_array a h' ! k = (if k = i then get_array a h ! j
       else if k = j then get_array a h ! i
       else get_array a h ! k)"
 using assms unfolding swap.simps
-by (elim crel_elim_all)
+by (elim crel_elims)
  (auto simp: length_def)
 
 lemma rev_pointwise: assumes "crel (rev a i j) h h' r"
   shows "get_array a h' ! k = (if k < i then get_array a h ! k
       else if j < k then get_array a h ! k

     case True
     with 1[unfolded rev.simps[of a i j]]
     obtain h' where
       swp: "crel (swap a i j) h h' ()"
       and rev: "crel (rev a (i + 1) (j - 1)) h' h'' ()"
-      by (auto elim: crel_elim_all)
+      by (auto elim: crel_elims)
     from rev 1 True
     have eq: "?P a (i + 1) (j - 1) h' h''" by auto
 
     have "k < i \<or> i = k \<or> (i < k \<and> k < j) \<or> j = k \<or> j < k" by arith
     with True show ?thesis
       by (elim disjE) (auto simp: eq swap_pointwise[OF swp])
   next
     case False
     with 1[unfolded rev.simps[of a i j]]
     show ?thesis
-      by (cases "k = j") (auto elim: crel_elim_all)
+      by (cases "k = j") (auto elim: crel_elims)
   qed
 qed
 
 lemma rev_length:
   assumes "crel (rev a i j) h h' r"

     case True
     with 1[unfolded rev.simps[of a i j]]
     obtain h' where
       swp: "crel (swap a i j) h h' ()"
       and rev: "crel (rev a (i + 1) (j - 1)) h' h'' ()"
-      by (auto elim: crel_elim_all)
+      by (auto elim: crel_elims)
     from swp rev 1 True show ?thesis
       unfolding swap.simps
-      by (elim crel_elim_all) fastsimp
+      by (elim crel_elims) fastsimp
   next
     case False
     with 1[unfolded rev.simps[of a i j]]
     show ?thesis
-      by (auto elim: crel_elim_all)
+      by (auto elim: crel_elims)
   qed
 qed
 
 lemma rev2_rev': assumes "crel (rev a i j) h h' u"
   assumes "j < Array.length a h"

 lemma rev2_rev: 
   assumes "crel (rev a 0 (Array.length a h - 1)) h h' u"
   shows "get_array a h' = List.rev (get_array a h)"
   using rev2_rev'[OF assms] rev_length[OF assms] assms
     by (cases "Array.length a h = 0", auto simp add: Array.length_def
-      subarray_def sublist'_all rev.simps[where j=0] elim!: crel_elim_all)
+      subarray_def sublist'_all rev.simps[where j=0] elim!: crel_elims)
   (drule sym[of "List.length (get_array a h)"], simp)
 
 end