src/HOLCF/Cprod.thy
changeset 16750 282d092b1dbd
parent 16553 aa36d41e4263
child 16916 da331e0a4a81
     1.1 --- a/src/HOLCF/Cprod.thy	Thu Jul 07 21:41:08 2005 +0200
     1.2 +++ b/src/HOLCF/Cprod.thy	Fri Jul 08 02:37:42 2005 +0200
     1.3 @@ -285,9 +285,12 @@
     1.4  apply (simp add: cont_fst cont_snd cpair_eq_pair)
     1.5  done
     1.6  
     1.7 -lemma less_cprod: "p1 \<sqsubseteq> p2 = (cfst\<cdot>p1 \<sqsubseteq> cfst\<cdot>p2 \<and> csnd\<cdot>p1 \<sqsubseteq> csnd\<cdot>p2)"
     1.8 +lemma less_cprod: "x \<sqsubseteq> y = (cfst\<cdot>x \<sqsubseteq> cfst\<cdot>y \<and> csnd\<cdot>x \<sqsubseteq> csnd\<cdot>y)"
     1.9  by (simp add: less_cprod_def cfst_def csnd_def cont_fst cont_snd)
    1.10  
    1.11 +lemma eq_cprod: "(x = y) = (cfst\<cdot>x = cfst\<cdot>y \<and> csnd\<cdot>x = csnd\<cdot>y)"
    1.12 +by (auto simp add: po_eq_conv less_cprod)
    1.13 +
    1.14  lemma lub_cprod2: 
    1.15    "chain S \<Longrightarrow> range S <<| <\<Squnion>i. cfst\<cdot>(S i), \<Squnion>i. csnd\<cdot>(S i)>"
    1.16  apply (simp add: cpair_eq_pair cfst_def csnd_def cont_fst cont_snd)