--- a/src/HOL/Old_Number_Theory/Gauss.thy Thu Jan 13 21:50:13 2011 +0100
+++ b/src/HOL/Old_Number_Theory/Gauss.thy Thu Jan 13 23:50:16 2011 +0100
@@ -79,10 +79,10 @@
by (auto simp add: C_def finite_B)
lemma finite_D: "finite (D)"
-by (auto simp add: D_def finite_Int finite_C)
+by (auto simp add: D_def finite_C)
lemma finite_E: "finite (E)"
-by (auto simp add: E_def finite_Int finite_C)
+by (auto simp add: E_def finite_C)
lemma finite_F: "finite (F)"
by (auto simp add: F_def finite_E)
@@ -125,11 +125,11 @@
with zcong_less_eq [of x y p] p_minus_one_l
order_le_less_trans [of x "(p - 1) div 2" p]
order_le_less_trans [of y "(p - 1) div 2" p] show "x = y"
- by (simp add: prems p_minus_one_l p_g_0)
+ by (simp add: b c d e p_minus_one_l p_g_0)
qed
lemma SR_B_inj: "inj_on (StandardRes p) B"
- apply (auto simp add: B_def StandardRes_def inj_on_def A_def prems)
+ apply (auto simp add: B_def StandardRes_def inj_on_def A_def)
proof -
fix x fix y
assume a: "x * a mod p = y * a mod p"
@@ -146,7 +146,7 @@
with zcong_less_eq [of x y p] p_minus_one_l
order_le_less_trans [of x "(p - 1) div 2" p]
order_le_less_trans [of y "(p - 1) div 2" p] have "x = y"
- by (simp add: prems p_minus_one_l p_g_0)
+ by (simp add: b c d e p_minus_one_l p_g_0)
then have False
by (simp add: f)
then show "a = 0"