--- a/src/HOL/NSA/HyperDef.thy Thu Mar 29 14:39:05 2012 +0200
+++ b/src/HOL/NSA/HyperDef.thy Thu Mar 29 14:42:55 2012 +0200
@@ -538,7 +538,7 @@
lemma hyperpow_minus_one2 [simp]:
"\<And>n. -1 pow (2*n) = (1::hypreal)"
-by transfer (rule power_m1_even)
+by transfer (rule power_minus1_even)
lemma hyperpow_less_le:
"!!r n N. [|(0::hypreal) \<le> r; r \<le> 1; n < N|] ==> r pow N \<le> r pow n"
--- a/src/HOL/Nat_Numeral.thy Thu Mar 29 14:39:05 2012 +0200
+++ b/src/HOL/Nat_Numeral.thy Thu Mar 29 14:42:55 2012 +0200
@@ -200,12 +200,6 @@
lemma Let_Suc [simp]: "Let (Suc n) f == f (Suc n)"
by (fact Let_def)
-lemma power_m1_even: "(-1) ^ (2*n) = (1::'a::ring_1)"
- by (fact power_minus1_even) (* FIXME: duplicate *)
-
-lemma power_m1_odd: "(-1) ^ Suc(2*n) = (-1::'a::ring_1)"
- by (fact power_minus1_odd) (* FIXME: duplicate *)
-
subsection{*Literal arithmetic and @{term of_nat}*}