--- a/src/HOL/OrderedGroup.thy Wed Jan 28 16:57:36 2009 +0100
+++ b/src/HOL/OrderedGroup.thy Wed Jan 28 17:12:25 2009 +0100
@@ -1202,7 +1202,6 @@
qed
have abs_leI: "\<And>a b. a \<le> b \<Longrightarrow> - a \<le> b \<Longrightarrow> \<bar>a\<bar> \<le> b"
by (simp add: abs_lattice le_supI)
-<<<<<<< local
fix a b
show "0 \<le> \<bar>a\<bar>" by simp
show "a \<le> \<bar>a\<bar>"
@@ -1223,36 +1222,6 @@
by (drule_tac abs_leI, auto)
with g[symmetric] show ?thesis by simp
qed
-=======
- show ?thesis
- proof
- fix a
- show "0 \<le> \<bar>a\<bar>" by simp
- next
- fix a
- show "a \<le> \<bar>a\<bar>" by (auto simp add: abs_lattice)
- next
- fix a
- show "\<bar>-a\<bar> = \<bar>a\<bar>" by (simp add: abs_lattice sup_commute)
- next
- fix a b
- show "a \<le> b \<Longrightarrow> - a \<le> b \<Longrightarrow> \<bar>a\<bar> \<le> b" by (erule abs_leI)
- next
- fix a b
- show "\<bar>a + b\<bar> \<le> \<bar>a\<bar> + \<bar>b\<bar>"
- proof -
- have g:"abs a + abs b = sup (a+b) (sup (-a-b) (sup (-a+b) (a + (-b))))" (is "_=sup ?m ?n")
- by (simp add: abs_lattice add_sup_inf_distribs sup_ACI diff_minus)
- have a:"a+b <= sup ?m ?n" by (simp)
- have b:"-a-b <= ?n" by (simp)
- have c:"?n <= sup ?m ?n" by (simp)
- from b c have d: "-a-b <= sup ?m ?n" by(rule order_trans)
- have e:"-a-b = -(a+b)" by (simp add: diff_minus)
- from a d e have "abs(a+b) <= sup ?m ?n" by (drule_tac abs_leI, auto)
- with g[symmetric] show ?thesis by simp
- qed
- qed auto
->>>>>>> other
qed
end