src/HOL/Dense_Linear_Order.thy
changeset 23915 fcbee3512a99
parent 23902 c69069242a51
child 24081 84a5a6267d60
equal deleted inserted replaced
23914:3e0424305fa4 23915:fcbee3512a99
   144   by dlo
   144   by dlo
   145 
   145 
   146 lemma "\<forall>(a::'a::ordered_field) b. (\<exists>x. a < x \<and> x< b) \<longleftrightarrow> (a < b)"
   146 lemma "\<forall>(a::'a::ordered_field) b. (\<exists>x. a < x \<and> x< b) \<longleftrightarrow> (a < b)"
   147   by dlo
   147   by dlo
   148 
   148 
   149 section {* Contructive dense linear orders yield QE for linear arithmetic over ordered Fields -- see Arith_Tools.thy *}
   149 section {* Contructive dense linear orders yield QE for linear arithmetic over ordered Fields -- see @{text "Arith_Tools.thy"} *}
   150 
   150 
   151 context Linorder
   151 context Linorder
   152 begin
   152 begin
   153 
   153 
   154 text{* Theorems for @{text "\<exists>z. \<forall>x. x \<sqsubset> z \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>-\<infinity>\<^esub>)"}*}
   154 text{* Theorems for @{text "\<exists>z. \<forall>x. x \<sqsubset> z \<longrightarrow> (P x \<longleftrightarrow> P\<^bsub>-\<infinity>\<^esub>)"}*}