diff -r f2e51e704a96 -r ab2e862263e7 src/HOL/Power.thy --- a/src/HOL/Power.thy Thu Oct 29 15:40:52 2015 +0100 +++ b/src/HOL/Power.thy Mon Nov 02 11:56:28 2015 +0100 @@ -283,6 +283,9 @@ by (simp del: power_Suc add: power_Suc2 mult.assoc) qed +lemma power_minus': "NO_MATCH 1 x \ (-x) ^ n = (-1)^n * x ^ n" + by (rule power_minus) + lemma power_minus_Bit0: "(- x) ^ numeral (Num.Bit0 k) = x ^ numeral (Num.Bit0 k)" by (induct k, simp_all only: numeral_class.numeral.simps power_add @@ -307,7 +310,7 @@ lemma power_minus1_odd: "(- 1) ^ Suc (2*n) = -1" by simp - + lemma power_minus_even [simp]: "(-a) ^ (2*n) = a ^ (2*n)" by (simp add: power_minus [of a])