--- a/src/HOL/Bit_Operations.thy Fri Jan 12 17:00:35 2024 +0100
+++ b/src/HOL/Bit_Operations.thy Sat Jan 13 19:50:12 2024 +0000
@@ -10,7 +10,7 @@
subsection \<open>Abstract bit structures\<close>
class semiring_bits = semiring_parity +
- assumes bits_induct [case_names stable rec]:
+ assumes bit_induct [case_names stable rec]:
\<open>(\<And>a. a div 2 = a \<Longrightarrow> P a)
\<Longrightarrow> (\<And>a b. P a \<Longrightarrow> (of_bool b + 2 * a) div 2 = a \<Longrightarrow> P (of_bool b + 2 * a))
\<Longrightarrow> P a\<close>
@@ -123,7 +123,7 @@
lemma bit_iff_idd_imp_stable:
\<open>a div 2 = a\<close> if \<open>\<And>n. bit a n \<longleftrightarrow> odd a\<close>
-using that proof (induction a rule: bits_induct)
+using that proof (induction a rule: bit_induct)
case (stable a)
then show ?case
by simp
@@ -192,7 +192,7 @@
then show ?thesis
by (rule that[unfolded possible_bit_def])
qed
- then show ?thesis proof (induction a arbitrary: b rule: bits_induct)
+ then show ?thesis proof (induction a arbitrary: b rule: bit_induct)
case (stable a)
from stable(2) [of 0] have **: \<open>even b \<longleftrightarrow> even a\<close>
by (simp add: bit_0)
@@ -3719,7 +3719,7 @@
\<^item> Equality rule: @{thm bit_eqI [where ?'a = int, no_vars]}
- \<^item> Induction rule: @{thm bits_induct [where ?'a = int, no_vars]}
+ \<^item> Induction rule: @{thm bit_induct [where ?'a = int, no_vars]}
\<^item> Typical operations are characterized as follows:
--- a/src/HOL/Code_Numeral.thy Fri Jan 12 17:00:35 2024 +0100
+++ b/src/HOL/Code_Numeral.thy Sat Jan 13 19:50:12 2024 +0000
@@ -348,7 +348,7 @@
is take_bit .
instance by (standard; transfer)
- (fact bit_eq_rec bits_induct bit_iff_odd push_bit_eq_mult drop_bit_eq_div take_bit_eq_mod
+ (fact bit_eq_rec bit_induct bit_iff_odd push_bit_eq_mult drop_bit_eq_div take_bit_eq_mod
bits_div_0 bits_div_by_1 bits_mod_div_trivial even_succ_div_2
exp_div_exp_eq div_exp_eq mod_exp_eq mult_exp_mod_exp_eq div_exp_mod_exp_eq
even_mask_div_iff even_mult_exp_div_exp_iff
@@ -1107,7 +1107,7 @@
is take_bit .
instance by (standard; transfer)
- (fact bit_eq_rec bits_induct bit_iff_odd push_bit_eq_mult drop_bit_eq_div take_bit_eq_mod
+ (fact bit_eq_rec bit_induct bit_iff_odd push_bit_eq_mult drop_bit_eq_div take_bit_eq_mod
bits_div_0 bits_div_by_1 bits_mod_div_trivial even_succ_div_2
exp_div_exp_eq div_exp_eq mod_exp_eq mult_exp_mod_exp_eq div_exp_mod_exp_eq
even_mask_div_iff even_mult_exp_div_exp_iff and_rec or_rec xor_rec