# HG changeset patch # User haftmann # Date 1476603063 -7200 # Node ID de5cd9217d4c929b09e393cdc9637baf5f250b66 # Parent b60a9752b6d097412291f67739ed1822c43b8111 added lemma diff -r b60a9752b6d0 -r de5cd9217d4c src/HOL/Rings.thy --- a/src/HOL/Rings.thy Sun Oct 16 09:31:03 2016 +0200 +++ b/src/HOL/Rings.thy Sun Oct 16 09:31:03 2016 +0200 @@ -1918,6 +1918,10 @@ lemma sgn_less [simp]: "sgn a < 0 \ a < 0" unfolding sgn_if by auto +lemma abs_sgn_eq_1 [simp]: + "a \ 0 \ \sgn a\ = 1" + by (simp add: abs_if) + lemma abs_sgn_eq: "\sgn a\ = (if a = 0 then 0 else 1)" by (simp add: sgn_if)