diff -r 143f58bb34f9 -r 0909deb8059b src/HOL/Old_Number_Theory/Legacy_GCD.thy --- a/src/HOL/Old_Number_Theory/Legacy_GCD.thy Thu May 26 16:57:14 2016 +0200 +++ b/src/HOL/Old_Number_Theory/Legacy_GCD.thy Thu May 26 17:51:22 2016 +0200 @@ -16,7 +16,7 @@ subsection \Specification of GCD on nats\ definition - is_gcd :: "nat \ nat \ nat \ bool" where -- \@{term gcd} as a relation\ + is_gcd :: "nat \ nat \ nat \ bool" where \ \@{term gcd} as a relation\ "is_gcd m n p \ p dvd m \ p dvd n \ (\d. d dvd m \ d dvd n \ d dvd p)" @@ -69,7 +69,7 @@ declare gcd.simps [simp del] text \ - \medskip @{term "gcd m n"} divides @{text m} and @{text n}. The + \medskip @{term "gcd m n"} divides \m\ and \n\. The conjunctions don't seem provable separately. \ @@ -130,7 +130,7 @@ \ lemma gcd_mult_distrib2: "k * gcd m n = gcd (k * m) (k * n)" - -- \@{cite \page 27\ davenport92}\ + \ \@{cite \page 27\ davenport92}\ apply (induct m n rule: gcd_induct) apply simp apply (case_tac "k = 0") @@ -697,7 +697,7 @@ done lemmas zgcd_ac = zgcd_assoc zgcd_commute zgcd_left_commute - -- \addition is an AC-operator\ + \ \addition is an AC-operator\ lemma zgcd_zmult_distrib2: "0 \ k ==> k * zgcd m n = zgcd (k * m) (k * n)" by (simp del: minus_mult_right [symmetric]