
diff -r 75f5c63f6cfa -r d8661799afb2 src/HOL/SPARK/Manual/Reference.thy
--- a/src/HOL/SPARK/Manual/Reference.thy	Wed Oct 28 08:41:07 2020 +0100
+++ b/src/HOL/SPARK/Manual/Reference.thy	Thu Oct 29 09:59:40 2020 +0000
@@ -1,8 +1,11 @@
 (*<*)
 theory Reference
-imports "HOL-SPARK.SPARK" "HOL-Word.Bits_Int"
+imports "HOL-SPARK.SPARK"
 begin
 
+lemma AND_mod: "x AND (2 ^ n - 1) = x mod 2 ^ n" for x :: int
+  by (simp flip: mask_eq_exp_minus_1 take_bit_eq_mask take_bit_eq_mod)
+
 syntax (my_constrain output)
   "_constrain" :: "logic => type => logic" ("_ :: _" [4, 0] 3)
 (*>*)




