# HG changeset patch # User bulwahn # Date 1503808021 -7200 # Node ID 2b49d4888cb8d4bc54f1f1458eafb9262ada3673 # Parent e5b1d4d55bf623897da7425cb3e9b0625a883c64 another fact on (- 1) ^ _ diff -r e5b1d4d55bf6 -r 2b49d4888cb8 src/HOL/Parity.thy --- a/src/HOL/Parity.thy Thu Aug 31 21:48:03 2017 +0200 +++ b/src/HOL/Parity.thy Sun Aug 27 06:27:01 2017 +0200 @@ -242,6 +242,9 @@ lemma neg_one_odd_power [simp]: "odd n \ (- 1) ^ n = - 1" by simp +lemma neg_one_power_add_eq_neg_one_power_diff: "k \ n \ (- 1) ^ (n + k) = (- 1) ^ (n - k)" + by (cases "even (n + k)") auto + end context linordered_idom