# HG changeset patch # User haftmann # Date 1560501267 0 # Node ID e939ea997f5fc2c99d6525e3f876a7b13c009c28 # Parent c832d431636b3b7871d62c2f8dbd0a7393f42c04 dropped weaker legacy alias diff -r c832d431636b -r e939ea997f5f src/HOL/Parity.thy --- a/src/HOL/Parity.thy Fri Jun 14 08:34:27 2019 +0000 +++ b/src/HOL/Parity.thy Fri Jun 14 08:34:27 2019 +0000 @@ -1016,14 +1016,4 @@ "drop_bit n (Suc 0) = of_bool (n = 0)" using drop_bit_of_1 [where ?'a = nat] by simp - -subsection \Legacy\ - -lemma parity_induct [case_names zero even odd]: - assumes zero: "P 0" - assumes even: "\n. P n \ P (2 * n)" - assumes odd: "\n. P n \ P (Suc (2 * n))" - shows "P n" - using assms by (rule nat_parity_induct) - end diff -r c832d431636b -r e939ea997f5f src/HOL/ex/Bit_Lists.thy --- a/src/HOL/ex/Bit_Lists.thy Fri Jun 14 08:34:27 2019 +0000 +++ b/src/HOL/ex/Bit_Lists.thy Fri Jun 14 08:34:27 2019 +0000 @@ -61,12 +61,12 @@ lemma not_last_bits_of_nat [simp]: "\ last (bits_of (of_nat n))" - by (induction n rule: parity_induct) + by (induction n rule: nat_parity_induct) (use of_nat_neq_0 in \simp_all add: algebra_simps\) lemma of_unsigned_bits_of_nat: "of_unsigned (bits_of (of_nat n)) = of_nat n" - by (induction n rule: parity_induct) + by (induction n rule: nat_parity_induct) (use of_nat_neq_0 in \simp_all add: algebra_simps\) end @@ -106,7 +106,7 @@ lemma last_bits_of_neg_of_nat [simp]: "last (bits_of (- 1 - of_nat n))" -proof (induction n rule: parity_induct) +proof (induction n rule: nat_parity_induct) case zero then show ?case by simp @@ -132,7 +132,7 @@ "of_signed (bits_of (- 1 - of_nat n)) = - 1 - of_nat n" proof - have "of_unsigned (map Not (bits_of (- 1 - of_nat n))) = of_nat n" - proof (induction n rule: parity_induct) + proof (induction n rule: nat_parity_induct) case zero then show ?case by simp