diff -r 143f58bb34f9 -r 0909deb8059b src/HOL/Old_Number_Theory/WilsonBij.thy --- a/src/HOL/Old_Number_Theory/WilsonBij.thy Thu May 26 16:57:14 2016 +0200 +++ b/src/HOL/Old_Number_Theory/WilsonBij.thy Thu May 26 17:51:22 2016 +0200 @@ -47,7 +47,7 @@ lemma inv_not_0: "zprime p ==> 1 < a ==> a < p - 1 ==> inv p a \ 0" - -- \same as @{text WilsonRuss}\ + \ \same as \WilsonRuss\\ apply safe apply (cut_tac a = a and p = p in inv_is_inv) apply (unfold zcong_def) @@ -56,7 +56,7 @@ lemma inv_not_1: "zprime p ==> 1 < a ==> a < p - 1 ==> inv p a \ 1" - -- \same as @{text WilsonRuss}\ + \ \same as \WilsonRuss\\ apply safe apply (cut_tac a = a and p = p in inv_is_inv) prefer 4 @@ -67,7 +67,7 @@ done lemma aux: "[a * (p - 1) = 1] (mod p) = [a = p - 1] (mod p)" - -- \same as @{text WilsonRuss}\ + \ \same as \WilsonRuss\\ apply (unfold zcong_def) apply (simp add: diff_diff_eq diff_diff_eq2 right_diff_distrib) apply (rule_tac s = "p dvd -((a + 1) + (p * -a))" in trans) @@ -81,7 +81,7 @@ lemma inv_not_p_minus_1: "zprime p ==> 1 < a ==> a < p - 1 ==> inv p a \ p - 1" - -- \same as @{text WilsonRuss}\ + \ \same as \WilsonRuss\\ apply safe apply (cut_tac a = a and p = p in inv_is_inv) apply auto @@ -93,7 +93,7 @@ text \ Below is slightly different as we don't expand @{term [source] inv} - but use ``@{text correct}'' theorems. + but use ``\correct\'' theorems. \ lemma inv_g_1: "zprime p ==> 1 < a ==> a < p - 1 ==> 1 < inv p a" @@ -111,7 +111,7 @@ lemma inv_less_p_minus_1: "zprime p ==> 1 < a ==> a < p - 1 ==> inv p a < p - 1" - -- \ditto\ + \ \ditto\ apply (subst order_less_le) apply (simp add: inv_not_p_minus_1 inv_less) done