# HG changeset patch # User huffman # Date 1215101739 -7200 # Node ID a89d755b029d010f5ed476c33a2b72d3d8df029b # Parent 83f9734241169efbee8f8509c2cc1454005d511a move proofs of add_left_cancel and add_right_cancel into the correct locale diff -r 83f973424116 -r a89d755b029d src/HOL/OrderedGroup.thy --- a/src/HOL/OrderedGroup.thy Thu Jul 03 18:03:10 2008 +0200 +++ b/src/HOL/OrderedGroup.thy Thu Jul 03 18:15:39 2008 +0200 @@ -106,6 +106,17 @@ class cancel_semigroup_add = semigroup_add + assumes add_left_imp_eq: "a + b = a + c \ b = c" assumes add_right_imp_eq: "b + a = c + a \ b = c" +begin + +lemma add_left_cancel [simp]: + "a + b = a + c \ b = c" + by (blast dest: add_left_imp_eq) + +lemma add_right_cancel [simp]: + "b + a = c + a \ b = c" + by (blast dest: add_right_imp_eq) + +end class cancel_ab_semigroup_add = ab_semigroup_add + assumes add_imp_eq: "a + b = a + c \ b = c" @@ -125,19 +136,6 @@ end -context cancel_ab_semigroup_add -begin - -lemma add_left_cancel [simp]: - "a + b = a + c \ b = c" - by (blast dest: add_left_imp_eq) - -lemma add_right_cancel [simp]: - "b + a = c + a \ b = c" - by (blast dest: add_right_imp_eq) - -end - subsection {* Groups *} class group_add = minus + uminus + monoid_add +