diff -r 19f627407264 -r ccab07d1196c src/HOL/Euclidean_Division.thy --- a/src/HOL/Euclidean_Division.thy Sat Dec 02 16:50:53 2017 +0000 +++ b/src/HOL/Euclidean_Division.thy Sat Dec 02 16:50:53 2017 +0000 @@ -1432,7 +1432,7 @@ then int (m div n) else - int (m div n + of_bool (\ n dvd m)))" by (auto simp add: divide_int_def sgn_0_0 sgn_1_pos sgn_mult abs_mult - nat_mult_distrib dvd_int_iff) + nat_mult_distrib) instance proof fix k :: int show "k div 0 = 0" @@ -1460,7 +1460,7 @@ fix q assume "q dvd m" "q dvd n" then have "int q dvd int m" "int q dvd int n" - by (simp_all add: zdvd_int) + by simp_all with \?P\ have "is_unit (int q)" by (rule coprime_common_divisor) then show "is_unit q" @@ -1473,7 +1473,7 @@ fix k assume "k dvd int m" "k dvd int n" then have "nat \k\ dvd m" "nat \k\ dvd n" - by (simp_all add: zdvd_int) + by simp_all with \?Q\ have "is_unit (nat \k\)" by (rule coprime_common_divisor) then show "is_unit k" @@ -1525,7 +1525,7 @@ then sgn l * int (m mod n) else sgn l * (int (n * of_bool (\ n dvd m)) - int (m mod n)))" by (auto simp add: modulo_int_def sgn_0_0 sgn_1_pos sgn_mult abs_mult - nat_mult_distrib dvd_int_iff) + nat_mult_distrib) instance proof fix k l :: int @@ -1574,7 +1574,7 @@ by (blast intro: int_sgnE elim: that) with that show ?thesis by (simp add: modulo_int_unfold sgn_0_0 sgn_1_pos sgn_1_neg - sgn_mult mod_eq_0_iff_dvd int_dvd_iff) + sgn_mult mod_eq_0_iff_dvd) qed instance proof