--- a/src/HOL/Decision_Procs/Approximation.thy Sun Nov 13 20:28:22 2011 +0100
+++ b/src/HOL/Decision_Procs/Approximation.thy Mon Nov 14 09:25:05 2011 +0100
@@ -1178,15 +1178,6 @@
from *[OF this] show thesis by blast
qed
-lemma float_remove_real_numeral[simp]: "(number_of k :: float) = (number_of k :: real)"
-proof -
- have "(number_of k :: float) = real k"
- unfolding number_of_float_def real_of_float_def pow2_def by auto
- also have "\<dots> = (number_of k :: int)"
- by (simp add: number_of_is_id)
- finally show ?thesis by auto
-qed
-
lemma cos_periodic_nat[simp]: fixes n :: nat shows "cos (x + n * (2 * pi)) = cos x"
proof (induct n arbitrary: x)
case (Suc n)
--- a/src/HOL/Old_Number_Theory/Euler.thy Sun Nov 13 20:28:22 2011 +0100
+++ b/src/HOL/Old_Number_Theory/Euler.thy Mon Nov 14 09:25:05 2011 +0100
@@ -85,7 +85,7 @@
apply (auto simp add: MultInvPair_def)
apply (subgoal_tac "~ (StandardRes p j = StandardRes p (a * MultInv p j))")
apply auto
- apply (metis MultInvPair_distinct Pls_def StandardRes_def aux number_of_is_id one_is_num_one)
+ apply (metis MultInvPair_distinct StandardRes_def aux)
done
@@ -227,7 +227,7 @@
lemma Euler_part1: "[| 2 < p; zprime p; ~([x = 0](mod p));
~(QuadRes p x) |] ==>
[x^(nat (((p) - 1) div 2)) = -1](mod p)"
- by (metis Wilson_Russ number_of_is_id zcong_sym zcong_trans zfact_prop)
+ by (metis Wilson_Russ zcong_sym zcong_trans zfact_prop)
text {* \medskip Prove another part of Euler Criterion: *}
@@ -280,13 +280,13 @@
apply (subgoal_tac "p \<in> zOdd")
apply (auto simp add: QuadRes_def)
prefer 2
- apply (metis number_of_is_id numeral_1_eq_1 zprime_zOdd_eq_grt_2)
+ apply (metis zprime_zOdd_eq_grt_2)
apply (frule aux__1, auto)
apply (drule_tac z = "nat ((p - 1) div 2)" in zcong_zpower)
apply (auto simp add: zpower_zpower)
apply (rule zcong_trans)
apply (auto simp add: zcong_sym [of "x ^ nat ((p - 1) div 2)"])
- apply (metis Little_Fermat even_div_2_prop2 mult_Bit0 number_of_is_id odd_minus_one_even one_is_num_one mult_1 aux__2)
+ apply (metis Little_Fermat even_div_2_prop2 odd_minus_one_even mult_1 aux__2)
done
--- a/src/HOL/Old_Number_Theory/EulerFermat.thy Sun Nov 13 20:28:22 2011 +0100
+++ b/src/HOL/Old_Number_Theory/EulerFermat.thy Mon Nov 14 09:25:05 2011 +0100
@@ -142,7 +142,7 @@
prefer 2
apply (subst zdvd_iff_zgcd [symmetric])
apply (rule_tac [4] zgcd_zcong_zgcd)
- apply (simp_all add: zcong_sym)
+ apply (simp_all (no_asm_use) add: zcong_sym)
done