# HG changeset patch # User huffman # Date 1237840012 25200 # Node ID 0047f57f6669ff1119e8453b04064fcfbb547150 # Parent 55ef8e0459315463e19f9bc3c436b661d2dd2761 lemmas add_sign_intros diff -r 55ef8e045931 -r 0047f57f6669 src/HOL/OrderedGroup.thy --- a/src/HOL/OrderedGroup.thy Mon Mar 23 19:01:34 2009 +0100 +++ b/src/HOL/OrderedGroup.thy Mon Mar 23 13:26:52 2009 -0700 @@ -466,7 +466,7 @@ then show ?thesis by simp qed -lemma add_neg_nonpos: +lemma add_neg_nonpos: assumes "a < 0" and "b \ 0" shows "a + b < 0" proof - have "a + b < 0 + 0" @@ -494,6 +494,10 @@ then show ?thesis by simp qed +lemmas add_sign_intros = + add_pos_nonneg add_pos_pos add_nonneg_pos add_nonneg_nonneg + add_neg_nonpos add_neg_neg add_nonpos_neg add_nonpos_nonpos + lemma add_nonneg_eq_0_iff: assumes x: "0 \ x" and y: "0 \ y" shows "x + y = 0 \ x = 0 \ y = 0"