# HG changeset patch
# User haftmann
# Date 1277908093 -7200
# Node ID 8e33b9d04a82ddeabe12aa026e4364a8d2692dc0
# Parent  847e95ca9b0a4c48553957744e79cd36a9f5e58c
use existing bit type from theory Bit

diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/BinBoolList.thy
--- a/src/HOL/Word/BinBoolList.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/BinBoolList.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -53,7 +53,7 @@
 
 lemma bin_to_bl_aux_Bit_minus_simp [simp]:
   "0 < n ==> bin_to_bl_aux n (w BIT b) bl = 
-    bin_to_bl_aux (n - 1) w ((b = bit.B1) # bl)"
+    bin_to_bl_aux (n - 1) w ((b = 1) # bl)"
   by (cases n) auto
 
 lemma bin_to_bl_aux_Bit0_minus_simp [simp]:
@@ -387,15 +387,15 @@
   by (cases xs) auto
 
 lemma last_bin_last': 
-  "size xs > 0 \<Longrightarrow> last xs = (bin_last (bl_to_bin_aux xs w) = bit.B1)" 
+  "size xs > 0 \<Longrightarrow> last xs = (bin_last (bl_to_bin_aux xs w) = 1)" 
   by (induct xs arbitrary: w) auto
 
 lemma last_bin_last: 
-  "size xs > 0 ==> last xs = (bin_last (bl_to_bin xs) = bit.B1)" 
+  "size xs > 0 ==> last xs = (bin_last (bl_to_bin xs) = 1)" 
   unfolding bl_to_bin_def by (erule last_bin_last')
   
 lemma bin_last_last: 
-  "bin_last w = (if last (bin_to_bl (Suc n) w) then bit.B1 else bit.B0)" 
+  "bin_last w = (if last (bin_to_bl (Suc n) w) then 1 else 0)" 
   apply (unfold bin_to_bl_def)
   apply simp
   apply (auto simp add: bin_to_bl_aux_alt)
@@ -815,7 +815,7 @@
 lemmas rbl_mult_Suc = lessI [THEN rbl_mult_gt]
 
 lemma rbbl_Cons: 
-  "b # rev (bin_to_bl n x) = rev (bin_to_bl (Suc n) (x BIT If b bit.B1 bit.B0))"
+  "b # rev (bin_to_bl n x) = rev (bin_to_bl (Suc n) (x BIT If b 1 0))"
   apply (unfold bin_to_bl_def)
   apply simp
   apply (simp add: bin_to_bl_aux_alt)
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/BinGeneral.thy
--- a/src/HOL/Word/BinGeneral.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/BinGeneral.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -9,27 +9,22 @@
 header {* Basic Definitions for Binary Integers *}
 
 theory BinGeneral
-imports Num_Lemmas
+imports Misc_Numeric Bit
 begin
 
 subsection {* Further properties of numerals *}
 
-datatype bit = B0 | B1
+definition Bit :: "int \<Rightarrow> bit \<Rightarrow> int" (infixl "BIT" 90) where
+  "k BIT b = bit_case 0 1 b + k + k"
 
-definition
-  Bit :: "int \<Rightarrow> bit \<Rightarrow> int" (infixl "BIT" 90) where
-  "k BIT b = (case b of B0 \<Rightarrow> 0 | B1 \<Rightarrow> 1) + k + k"
-
-lemma BIT_B0_eq_Bit0 [simp]: "w BIT B0 = Int.Bit0 w"
+lemma BIT_B0_eq_Bit0 [simp]: "w BIT 0 = Int.Bit0 w"
   unfolding Bit_def Bit0_def by simp
 
-lemma BIT_B1_eq_Bit1 [simp]: "w BIT B1 = Int.Bit1 w"
+lemma BIT_B1_eq_Bit1 [simp]: "w BIT 1 = Int.Bit1 w"
   unfolding Bit_def Bit1_def by simp
 
 lemmas BIT_simps = BIT_B0_eq_Bit0 BIT_B1_eq_Bit1
 
-hide_const (open) B0 B1
-
 lemma Min_ne_Pls [iff]:  
   "Int.Min ~= Int.Pls"
   unfolding Min_def Pls_def by auto
@@ -63,32 +58,32 @@
 lemmas BIT_eqI [intro!] = conjI [THEN BIT_eq_iff [THEN iffD2]]
 
 lemma less_Bits: 
-  "(v BIT b < w BIT c) = (v < w | v <= w & b = bit.B0 & c = bit.B1)"
+  "(v BIT b < w BIT c) = (v < w | v <= w & b = (0::bit) & c = (1::bit))"
   unfolding Bit_def by (auto split: bit.split)
 
 lemma le_Bits: 
-  "(v BIT b <= w BIT c) = (v < w | v <= w & (b ~= bit.B1 | c ~= bit.B0))" 
+  "(v BIT b <= w BIT c) = (v < w | v <= w & (b ~= (1::bit) | c ~= (0::bit)))" 
   unfolding Bit_def by (auto split: bit.split)
 
 lemma no_no [simp]: "number_of (number_of i) = i"
   unfolding number_of_eq by simp
 
 lemma Bit_B0:
-  "k BIT bit.B0 = k + k"
+  "k BIT (0::bit) = k + k"
    by (unfold Bit_def) simp
 
 lemma Bit_B1:
-  "k BIT bit.B1 = k + k + 1"
+  "k BIT (1::bit) = k + k + 1"
    by (unfold Bit_def) simp
   
-lemma Bit_B0_2t: "k BIT bit.B0 = 2 * k"
+lemma Bit_B0_2t: "k BIT (0::bit) = 2 * k"
   by (rule trans, rule Bit_B0) simp
 
-lemma Bit_B1_2t: "k BIT bit.B1 = 2 * k + 1"
+lemma Bit_B1_2t: "k BIT (1::bit) = 2 * k + 1"
   by (rule trans, rule Bit_B1) simp
 
 lemma B_mod_2': 
-  "X = 2 ==> (w BIT bit.B1) mod X = 1 & (w BIT bit.B0) mod X = 0"
+  "X = 2 ==> (w BIT (1::bit)) mod X = 1 & (w BIT (0::bit)) mod X = 0"
   apply (simp (no_asm) only: Bit_B0 Bit_B1)
   apply (simp add: z1pmod2)
   done
@@ -100,8 +95,8 @@
   unfolding numeral_simps number_of_is_id by simp
 
 lemma neB1E [elim!]:
-  assumes ne: "y \<noteq> bit.B1"
-  assumes y: "y = bit.B0 \<Longrightarrow> P"
+  assumes ne: "y \<noteq> (1::bit)"
+  assumes y: "y = (0::bit) \<Longrightarrow> P"
   shows "P"
   apply (rule y)
   apply (cases y rule: bit.exhaust, simp)
@@ -128,7 +123,7 @@
 subsection {* Destructors for binary integers *}
 
 definition bin_last :: "int \<Rightarrow> bit" where
-  "bin_last w = (if w mod 2 = 0 then bit.B0 else bit.B1)"
+  "bin_last w = (if w mod 2 = 0 then (0::bit) else (1::bit))"
 
 definition bin_rest :: "int \<Rightarrow> int" where
   "bin_rest w = w div 2"
@@ -144,21 +139,17 @@
   done
 
 primrec bin_nth where
-  Z: "bin_nth w 0 = (bin_last w = bit.B1)"
+  Z: "bin_nth w 0 = (bin_last w = (1::bit))"
   | Suc: "bin_nth w (Suc n) = bin_nth (bin_rest w) n"
 
 lemma bin_rl_simps [simp]:
-  "bin_rl Int.Pls = (Int.Pls, bit.B0)"
-  "bin_rl Int.Min = (Int.Min, bit.B1)"
-  "bin_rl (Int.Bit0 r) = (r, bit.B0)"
-  "bin_rl (Int.Bit1 r) = (r, bit.B1)"
+  "bin_rl Int.Pls = (Int.Pls, (0::bit))"
+  "bin_rl Int.Min = (Int.Min, (1::bit))"
+  "bin_rl (Int.Bit0 r) = (r, (0::bit))"
+  "bin_rl (Int.Bit1 r) = (r, (1::bit))"
   "bin_rl (r BIT b) = (r, b)"
   unfolding bin_rl_char by simp_all
 
-declare bin_rl_simps(1-4) [code]
-
-thm iffD1 [OF bin_rl_char bin_rl_def]
-
 lemma bin_rl_simp [simp]:
   "bin_rest w BIT bin_last w = w"
   by (simp add: iffD1 [OF bin_rl_char bin_rl_def])
@@ -212,35 +203,27 @@
   "bin_rest (w BIT b) = w"
   using bin_rl_simps bin_rl_def by auto
 
-declare bin_rest_simps(1-4) [code]
-
 lemma bin_last_simps [simp]: 
-  "bin_last Int.Pls = bit.B0"
-  "bin_last Int.Min = bit.B1"
-  "bin_last (Int.Bit0 w) = bit.B0"
-  "bin_last (Int.Bit1 w) = bit.B1"
+  "bin_last Int.Pls = (0::bit)"
+  "bin_last Int.Min = (1::bit)"
+  "bin_last (Int.Bit0 w) = (0::bit)"
+  "bin_last (Int.Bit1 w) = (1::bit)"
   "bin_last (w BIT b) = b"
   using bin_rl_simps bin_rl_def by auto
 
-declare bin_last_simps(1-4) [code]
-
 lemma bin_r_l_extras [simp]:
-  "bin_last 0 = bit.B0"
-  "bin_last (- 1) = bit.B1"
-  "bin_last -1 = bit.B1"
-  "bin_last 1 = bit.B1"
+  "bin_last 0 = (0::bit)"
+  "bin_last (- 1) = (1::bit)"
+  "bin_last -1 = (1::bit)"
+  "bin_last 1 = (1::bit)"
   "bin_rest 1 = 0"
   "bin_rest 0 = 0"
   "bin_rest (- 1) = - 1"
   "bin_rest -1 = -1"
-  apply (unfold number_of_Min)
-  apply (unfold Pls_def [symmetric] Min_def [symmetric])
-  apply (unfold numeral_1_eq_1 [symmetric])
-  apply (auto simp: number_of_eq) 
-  done
+  by (simp_all add: bin_last_def bin_rest_def)
 
 lemma bin_last_mod: 
-  "bin_last w = (if w mod 2 = 0 then bit.B0 else bit.B1)"
+  "bin_last w = (if w mod 2 = 0 then (0::bit) else (1::bit))"
   apply (case_tac w rule: bin_exhaust)
   apply (case_tac b)
    apply auto
@@ -261,10 +244,10 @@
   unfolding bin_rest_div [symmetric] by auto
 
 lemma Bit0_div2 [simp]: "(Int.Bit0 w) div 2 = w"
-  using Bit_div2 [where b=bit.B0] by simp
+  using Bit_div2 [where b="(0::bit)"] by simp
 
 lemma Bit1_div2 [simp]: "(Int.Bit1 w) div 2 = w"
-  using Bit_div2 [where b=bit.B1] by simp
+  using Bit_div2 [where b="(1::bit)"] by simp
 
 lemma bin_nth_lem [rule_format]:
   "ALL y. bin_nth x = bin_nth y --> x = y"
@@ -306,7 +289,7 @@
 lemma bin_nth_Min [simp]: "bin_nth Int.Min n"
   by (induct n) auto
 
-lemma bin_nth_0_BIT: "bin_nth (w BIT b) 0 = (b = bit.B1)"
+lemma bin_nth_0_BIT: "bin_nth (w BIT b) 0 = (b = (1::bit))"
   by auto
 
 lemma bin_nth_Suc_BIT: "bin_nth (w BIT b) (Suc n) = bin_nth w n"
@@ -317,11 +300,11 @@
 
 lemma bin_nth_minus_Bit0 [simp]:
   "0 < n ==> bin_nth (Int.Bit0 w) n = bin_nth w (n - 1)"
-  using bin_nth_minus [where b=bit.B0] by simp
+  using bin_nth_minus [where b="(0::bit)"] by simp
 
 lemma bin_nth_minus_Bit1 [simp]:
   "0 < n ==> bin_nth (Int.Bit1 w) n = bin_nth w (n - 1)"
-  using bin_nth_minus [where b=bit.B1] by simp
+  using bin_nth_minus [where b="(1::bit)"] by simp
 
 lemmas bin_nth_0 = bin_nth.simps(1)
 lemmas bin_nth_Suc = bin_nth.simps(2)
@@ -364,18 +347,18 @@
   by (simp add: bin_rec.simps)
 
 lemma bin_rec_Bit0:
-  "f3 Int.Pls bit.B0 f1 = f1 \<Longrightarrow>
-    bin_rec f1 f2 f3 (Int.Bit0 w) = f3 w bit.B0 (bin_rec f1 f2 f3 w)"
+  "f3 Int.Pls (0::bit) f1 = f1 \<Longrightarrow>
+    bin_rec f1 f2 f3 (Int.Bit0 w) = f3 w (0::bit) (bin_rec f1 f2 f3 w)"
   by (simp add: bin_rec_Pls bin_rec.simps [of _ _ _ "Int.Bit0 w"])
 
 lemma bin_rec_Bit1:
-  "f3 Int.Min bit.B1 f2 = f2 \<Longrightarrow>
-    bin_rec f1 f2 f3 (Int.Bit1 w) = f3 w bit.B1 (bin_rec f1 f2 f3 w)"
+  "f3 Int.Min (1::bit) f2 = f2 \<Longrightarrow>
+    bin_rec f1 f2 f3 (Int.Bit1 w) = f3 w (1::bit) (bin_rec f1 f2 f3 w)"
   by (simp add: bin_rec_Min bin_rec.simps [of _ _ _ "Int.Bit1 w"])
   
 lemma bin_rec_Bit:
-  "f = bin_rec f1 f2 f3  ==> f3 Int.Pls bit.B0 f1 = f1 ==> 
-    f3 Int.Min bit.B1 f2 = f2 ==> f (w BIT b) = f3 w b (f w)"
+  "f = bin_rec f1 f2 f3  ==> f3 Int.Pls (0::bit) f1 = f1 ==> 
+    f3 Int.Min (1::bit) f2 = f2 ==> f (w BIT b) = f3 w b (f w)"
   by (cases b, simp add: bin_rec_Bit0, simp add: bin_rec_Bit1)
 
 lemmas bin_rec_simps = refl [THEN bin_rec_Bit] bin_rec_Pls bin_rec_Min
@@ -411,7 +394,7 @@
   sbintrunc :: "nat => int => int" 
 primrec 
   Z : "sbintrunc 0 bin = 
-    (case bin_last bin of bit.B1 => Int.Min | bit.B0 => Int.Pls)"
+    (case bin_last bin of (1::bit) => Int.Min | (0::bit) => Int.Pls)"
   Suc : "sbintrunc (Suc n) bin = sbintrunc n (bin_rest bin) BIT (bin_last bin)"
 
 lemma sign_bintr:
@@ -445,7 +428,7 @@
 subsection "Simplifications for (s)bintrunc"
 
 lemma bit_bool:
-  "(b = (b' = bit.B1)) = (b' = (if b then bit.B1 else bit.B0))"
+  "(b = (b' = (1::bit))) = (b' = (if b then (1::bit) else (0::bit)))"
   by (cases b') auto
 
 lemmas bit_bool1 [simp] = refl [THEN bit_bool [THEN iffD1], symmetric]
@@ -472,16 +455,16 @@
   done
 
 lemma bin_nth_Bit:
-  "bin_nth (w BIT b) n = (n = 0 & b = bit.B1 | (EX m. n = Suc m & bin_nth w m))"
+  "bin_nth (w BIT b) n = (n = 0 & b = (1::bit) | (EX m. n = Suc m & bin_nth w m))"
   by (cases n) auto
 
 lemma bin_nth_Bit0:
   "bin_nth (Int.Bit0 w) n = (EX m. n = Suc m & bin_nth w m)"
-  using bin_nth_Bit [where b=bit.B0] by simp
+  using bin_nth_Bit [where b="(0::bit)"] by simp
 
 lemma bin_nth_Bit1:
   "bin_nth (Int.Bit1 w) n = (n = 0 | (EX m. n = Suc m & bin_nth w m))"
-  using bin_nth_Bit [where b=bit.B1] by simp
+  using bin_nth_Bit [where b="(1::bit)"] by simp
 
 lemma bintrunc_bintrunc_l:
   "n <= m ==> (bintrunc m (bintrunc n w) = bintrunc n w)"
@@ -518,11 +501,11 @@
 
 lemma bintrunc_Bit0 [simp]:
   "bintrunc (Suc n) (Int.Bit0 w) = Int.Bit0 (bintrunc n w)"
-  using bintrunc_BIT [where b=bit.B0] by simp
+  using bintrunc_BIT [where b="(0::bit)"] by simp
 
 lemma bintrunc_Bit1 [simp]:
   "bintrunc (Suc n) (Int.Bit1 w) = Int.Bit1 (bintrunc n w)"
-  using bintrunc_BIT [where b=bit.B1] by simp
+  using bintrunc_BIT [where b="(1::bit)"] by simp
 
 lemmas bintrunc_Sucs = bintrunc_Pls bintrunc_Min bintrunc_BIT
   bintrunc_Bit0 bintrunc_Bit1
@@ -538,11 +521,11 @@
 
 lemma sbintrunc_Suc_Bit0 [simp]:
   "sbintrunc (Suc n) (Int.Bit0 w) = Int.Bit0 (sbintrunc n w)"
-  using sbintrunc_Suc_BIT [where b=bit.B0] by simp
+  using sbintrunc_Suc_BIT [where b="(0::bit)"] by simp
 
 lemma sbintrunc_Suc_Bit1 [simp]:
   "sbintrunc (Suc n) (Int.Bit1 w) = Int.Bit1 (sbintrunc n w)"
-  using sbintrunc_Suc_BIT [where b=bit.B1] by simp
+  using sbintrunc_Suc_BIT [where b="(1::bit)"] by simp
 
 lemmas sbintrunc_Sucs = sbintrunc_Suc_Pls sbintrunc_Suc_Min sbintrunc_Suc_BIT
   sbintrunc_Suc_Bit0 sbintrunc_Suc_Bit1
@@ -556,11 +539,11 @@
                simplified bin_last_simps bin_rest_simps bit.simps, standard]
 
 lemmas sbintrunc_0_BIT_B0 [simp] = 
-  sbintrunc.Z [where bin="w BIT bit.B0", 
+  sbintrunc.Z [where bin="w BIT (0::bit)", 
                simplified bin_last_simps bin_rest_simps bit.simps, standard]
 
 lemmas sbintrunc_0_BIT_B1 [simp] = 
-  sbintrunc.Z [where bin="w BIT bit.B1", 
+  sbintrunc.Z [where bin="w BIT (1::bit)", 
                simplified bin_last_simps bin_rest_simps bit.simps, standard]
 
 lemma sbintrunc_0_Bit0 [simp]: "sbintrunc 0 (Int.Bit0 w) = Int.Pls"
@@ -936,12 +919,12 @@
 lemmas ls_splits = 
   prod.split split_split prod.split_asm split_split_asm split_if_asm
 
-lemma not_B1_is_B0: "y \<noteq> bit.B1 \<Longrightarrow> y = bit.B0"
+lemma not_B1_is_B0: "y \<noteq> (1::bit) \<Longrightarrow> y = (0::bit)"
   by (cases y) auto
 
 lemma B1_ass_B0: 
-  assumes y: "y = bit.B0 \<Longrightarrow> y = bit.B1"
-  shows "y = bit.B1"
+  assumes y: "y = (0::bit) \<Longrightarrow> y = (1::bit)"
+  shows "y = (1::bit)"
   apply (rule classical)
   apply (drule not_B1_is_B0)
   apply (erule y)
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/BinOperations.thy
--- a/src/HOL/Word/BinOperations.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/BinOperations.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -9,7 +9,7 @@
 header {* Bitwise Operations on Binary Integers *}
 
 theory BinOperations
-imports BinGeneral BitSyntax
+imports Bit_Operations BinGeneral
 begin
 
 subsection {* Logical operations *}
@@ -76,8 +76,8 @@
   unfolding BIT_simps [symmetric] int_xor_Bits by simp_all
 
 lemma int_xor_x_simps':
-  "w XOR (Int.Pls BIT bit.B0) = w"
-  "w XOR (Int.Min BIT bit.B1) = NOT w"
+  "w XOR (Int.Pls BIT 0) = w"
+  "w XOR (Int.Min BIT 1) = NOT w"
   apply (induct w rule: bin_induct)
        apply simp_all[4]
    apply (unfold int_xor_Bits)
@@ -109,8 +109,8 @@
   unfolding BIT_simps [symmetric] int_or_Bits by simp_all
 
 lemma int_or_x_simps': 
-  "w OR (Int.Pls BIT bit.B0) = w"
-  "w OR (Int.Min BIT bit.B1) = Int.Min"
+  "w OR (Int.Pls BIT 0) = w"
+  "w OR (Int.Min BIT 1) = Int.Min"
   apply (induct w rule: bin_induct)
        apply simp_all[4]
    apply (unfold int_or_Bits)
@@ -142,8 +142,8 @@
   unfolding BIT_simps [symmetric] int_and_Bits by simp_all
 
 lemma int_and_x_simps': 
-  "w AND (Int.Pls BIT bit.B0) = Int.Pls"
-  "w AND (Int.Min BIT bit.B1) = w"
+  "w AND (Int.Pls BIT 0) = Int.Pls"
+  "w AND (Int.Min BIT 1) = w"
   apply (induct w rule: bin_induct)
        apply simp_all[4]
    apply (unfold int_and_Bits)
@@ -384,7 +384,7 @@
 (** nth bit, set/clear **)
 
 lemma bin_nth_sc [simp]: 
-  "!!w. bin_nth (bin_sc n b w) n = (b = bit.B1)"
+  "!!w. bin_nth (bin_sc n b w) n = (b = 1)"
   by (induct n)  auto
 
 lemma bin_sc_sc_same [simp]: 
@@ -400,11 +400,11 @@
   done
 
 lemma bin_nth_sc_gen: 
-  "!!w m. bin_nth (bin_sc n b w) m = (if m = n then b = bit.B1 else bin_nth w m)"
+  "!!w m. bin_nth (bin_sc n b w) m = (if m = n then b = 1 else bin_nth w m)"
   by (induct n) (case_tac [!] m, auto)
   
 lemma bin_sc_nth [simp]:
-  "!!w. (bin_sc n (If (bin_nth w n) bit.B1 bit.B0) w) = w"
+  "!!w. (bin_sc n (If (bin_nth w n) 1 0) w) = w"
   by (induct n) auto
 
 lemma bin_sign_sc [simp]:
@@ -419,7 +419,7 @@
   done
 
 lemma bin_clr_le:
-  "!!w. bin_sc n bit.B0 w <= w"
+  "!!w. bin_sc n 0 w <= w"
   apply (induct n) 
    apply (case_tac [!] w rule: bin_exhaust)
    apply (auto simp del: BIT_simps)
@@ -428,7 +428,7 @@
   done
 
 lemma bin_set_ge:
-  "!!w. bin_sc n bit.B1 w >= w"
+  "!!w. bin_sc n 1 w >= w"
   apply (induct n) 
    apply (case_tac [!] w rule: bin_exhaust)
    apply (auto simp del: BIT_simps)
@@ -437,7 +437,7 @@
   done
 
 lemma bintr_bin_clr_le:
-  "!!w m. bintrunc n (bin_sc m bit.B0 w) <= bintrunc n w"
+  "!!w m. bintrunc n (bin_sc m 0 w) <= bintrunc n w"
   apply (induct n)
    apply simp
   apply (case_tac w rule: bin_exhaust)
@@ -448,7 +448,7 @@
   done
 
 lemma bintr_bin_set_ge:
-  "!!w m. bintrunc n (bin_sc m bit.B1 w) >= bintrunc n w"
+  "!!w m. bintrunc n (bin_sc m 1 w) >= bintrunc n w"
   apply (induct n)
    apply simp
   apply (case_tac w rule: bin_exhaust)
@@ -458,10 +458,10 @@
    apply (simp_all split: bit.split)
   done
 
-lemma bin_sc_FP [simp]: "bin_sc n bit.B0 Int.Pls = Int.Pls"
+lemma bin_sc_FP [simp]: "bin_sc n 0 Int.Pls = Int.Pls"
   by (induct n) auto
 
-lemma bin_sc_TM [simp]: "bin_sc n bit.B1 Int.Min = Int.Min"
+lemma bin_sc_TM [simp]: "bin_sc n 1 Int.Min = Int.Min"
   by (induct n) auto
   
 lemmas bin_sc_simps = bin_sc.Z bin_sc.Suc bin_sc_TM bin_sc_FP
@@ -481,7 +481,7 @@
 primrec bl_to_bin_aux :: "bool list \<Rightarrow> int \<Rightarrow> int" where
   Nil: "bl_to_bin_aux [] w = w"
   | Cons: "bl_to_bin_aux (b # bs) w = 
-      bl_to_bin_aux bs (w BIT (if b then bit.B1 else bit.B0))"
+      bl_to_bin_aux bs (w BIT (if b then 1 else 0))"
 
 definition bl_to_bin :: "bool list \<Rightarrow> int" where
   bl_to_bin_def : "bl_to_bin bs = bl_to_bin_aux bs Int.Pls"
@@ -489,7 +489,7 @@
 primrec bin_to_bl_aux :: "nat \<Rightarrow> int \<Rightarrow> bool list \<Rightarrow> bool list" where
   Z: "bin_to_bl_aux 0 w bl = bl"
   | Suc: "bin_to_bl_aux (Suc n) w bl =
-      bin_to_bl_aux n (bin_rest w) ((bin_last w = bit.B1) # bl)"
+      bin_to_bl_aux n (bin_rest w) ((bin_last w = 1) # bl)"
 
 definition bin_to_bl :: "nat \<Rightarrow> int \<Rightarrow> bool list" where
   bin_to_bl_def : "bin_to_bl n w = bin_to_bl_aux n w []"
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/WordArith.thy
--- a/src/HOL/Word/WordArith.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/WordArith.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -60,11 +60,11 @@
 lemmas word_0_wi_Pls = word_0_wi [folded Pls_def]
 lemmas word_0_no = word_0_wi_Pls [folded word_no_wi]
 
-lemma int_one_bin: "(1 :: int) == (Int.Pls BIT bit.B1)"
+lemma int_one_bin: "(1 :: int) == (Int.Pls BIT 1)"
   unfolding Pls_def Bit_def by auto
 
 lemma word_1_no: 
-  "(1 :: 'a :: len0 word) == number_of (Int.Pls BIT bit.B1)"
+  "(1 :: 'a :: len0 word) == number_of (Int.Pls BIT 1)"
   unfolding word_1_wi word_number_of_def int_one_bin by auto
 
 lemma word_m1_wi: "-1 == word_of_int -1" 
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/WordBitwise.thy
--- a/src/HOL/Word/WordBitwise.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/WordBitwise.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -386,12 +386,12 @@
   by (clarsimp simp add: nth_sbintr word_test_bit_def [symmetric])
 
 lemma word_lsb_no: 
-  "lsb (number_of bin :: 'a :: len word) = (bin_last bin = bit.B1)"
+  "lsb (number_of bin :: 'a :: len word) = (bin_last bin = 1)"
   unfolding word_lsb_alt test_bit_no by auto
 
 lemma word_set_no: 
   "set_bit (number_of bin::'a::len0 word) n b = 
-    number_of (bin_sc n (if b then bit.B1 else bit.B0) bin)"
+    number_of (bin_sc n (if b then 1 else 0) bin)"
   apply (unfold word_set_bit_def word_number_of_def [symmetric])
   apply (rule word_eqI)
   apply (clarsimp simp: word_size bin_nth_sc_gen number_of_is_id 
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/WordDefinition.thy
--- a/src/HOL/Word/WordDefinition.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/WordDefinition.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -8,7 +8,7 @@
 header {* Definition of Word Type *}
 
 theory WordDefinition
-imports Size BinBoolList TdThs
+imports Type_Length Misc_Typedef BinBoolList
 begin
 
 subsection {* Type definition *}
@@ -204,16 +204,16 @@
 
 definition
   word_set_bit_def: "set_bit a n x =
-   word_of_int (bin_sc n (If x bit.B1 bit.B0) (uint a))"
+   word_of_int (bin_sc n (If x 1 0) (uint a))"
 
 definition
   word_set_bits_def: "(BITS n. f n) = of_bl (bl_of_nth (len_of TYPE ('a)) f)"
 
 definition
-  word_lsb_def: "lsb a \<longleftrightarrow> bin_last (uint a) = bit.B1"
+  word_lsb_def: "lsb a \<longleftrightarrow> bin_last (uint a) = 1"
 
 definition shiftl1 :: "'a word \<Rightarrow> 'a word" where
-  "shiftl1 w = word_of_int (uint w BIT bit.B0)"
+  "shiftl1 w = word_of_int (uint w BIT 0)"
 
 definition shiftr1 :: "'a word \<Rightarrow> 'a word" where
   -- "shift right as unsigned or as signed, ie logical or arithmetic"
diff -r 847e95ca9b0a -r 8e33b9d04a82 src/HOL/Word/WordShift.thy
--- a/src/HOL/Word/WordShift.thy	Wed Jun 30 16:28:13 2010 +0200
+++ b/src/HOL/Word/WordShift.thy	Wed Jun 30 16:28:13 2010 +0200
@@ -13,7 +13,7 @@
 subsection "Bit shifting"
 
 lemma shiftl1_number [simp] :
-  "shiftl1 (number_of w) = number_of (w BIT bit.B0)"
+  "shiftl1 (number_of w) = number_of (w BIT 0)"
   apply (unfold shiftl1_def word_number_of_def)
   apply (simp add: word_ubin.norm_eq_iff [symmetric] word_ubin.eq_norm
               del: BIT_simps)
@@ -27,7 +27,7 @@
 
 lemmas shiftl1_def_u = shiftl1_def [folded word_number_of_def]
 
-lemma shiftl1_def_s: "shiftl1 w = number_of (sint w BIT bit.B0)"
+lemma shiftl1_def_s: "shiftl1 w = number_of (sint w BIT 0)"
   by (rule trans [OF _ shiftl1_number]) simp
 
 lemma shiftr1_0 [simp] : "shiftr1 0 = 0"