src/HOL/ex/Bit_Operations.thy

   then show \<open>bit (set_bit 0 a) m = bit (1 + 2 * (a div 2)) m\<close>
     by (simp add: bit_set_bit_iff bit_double_iff even_bit_succ_iff)
       (cases m, simp_all add: bit_Suc)
 qed
 
-lemma set_bit_Suc [simp]:
+lemma set_bit_Suc:
   \<open>set_bit (Suc n) a = a mod 2 + 2 * set_bit n (a div 2)\<close>
 proof (rule bit_eqI)
   fix m
   assume *: \<open>2 ^ m \<noteq> 0\<close>
   show \<open>bit (set_bit (Suc n) a) m \<longleftrightarrow> bit (a mod 2 + 2 * set_bit n (a div 2)) m\<close>

   then show \<open>bit (unset_bit 0 a) m = bit (2 * (a div 2)) m\<close>
     by (simp add: bit_unset_bit_iff bit_double_iff)
       (cases m, simp_all add: bit_Suc)
 qed
 
-lemma unset_bit_Suc [simp]:
+lemma unset_bit_Suc:
   \<open>unset_bit (Suc n) a = a mod 2 + 2 * unset_bit n (a div 2)\<close>
 proof (rule bit_eqI)
   fix m
   assume *: \<open>2 ^ m \<noteq> 0\<close>
   then show \<open>bit (unset_bit (Suc n) a) m \<longleftrightarrow> bit (a mod 2 + 2 * unset_bit n (a div 2)) m\<close>

   then show \<open>bit (flip_bit 0 a) m = bit (of_bool (even a) + 2 * (a div 2)) m\<close>
     by (simp add: bit_flip_bit_iff bit_double_iff even_bit_succ_iff)
       (cases m, simp_all add: bit_Suc)
 qed
 
-lemma flip_bit_Suc [simp]:
+lemma flip_bit_Suc:
   \<open>flip_bit (Suc n) a = a mod 2 + 2 * flip_bit n (a div 2)\<close>
 proof (rule bit_eqI)
   fix m
   assume *: \<open>2 ^ m \<noteq> 0\<close>
   show \<open>bit (flip_bit (Suc n) a) m \<longleftrightarrow> bit (a mod 2 + 2 * flip_bit n (a div 2)) m\<close>