src/HOL/Cardinals/Cardinal_Arithmetic.thy
changeset 54581 1502a1f707d9
parent 54481 5c9819d7713b
child 54794 e279c2ceb54c
equal deleted inserted replaced
54580:7b9336176a1c 54581:1502a1f707d9
   181 unfolding cpow_def by (metis Card_order_Pow cardSuc_ordLess_ordLeq card_of_Card_order)
   181 unfolding cpow_def by (metis Card_order_Pow cardSuc_ordLess_ordLeq card_of_Card_order)
   182 
   182 
   183 lemma cpow_cexp_ctwo: "cpow r =o ctwo ^c r"
   183 lemma cpow_cexp_ctwo: "cpow r =o ctwo ^c r"
   184 unfolding cpow_def ctwo_def cexp_def Field_card_of by (rule card_of_Pow_Func)
   184 unfolding cpow_def ctwo_def cexp_def Field_card_of by (rule card_of_Pow_Func)
   185 
   185 
   186 
       
   187 subsection {* Lists *}
       
   188 
       
   189 text {*
       
   190   The following collection of lemmas should be seen as an user interface to the HOL theory
       
   191   of cardinals. It is not expected to be complete in any sense, since its
       
   192   development was driven by demand arising from the development of the (co)datatype package.
       
   193 *}
       
   194 
       
   195 lemma clists_Cinfinite: "Cinfinite r \<Longrightarrow> clists r =o r"
       
   196 unfolding cinfinite_def clists_def by (blast intro: Card_order_lists_infinite)
       
   197 
       
   198 lemma Card_order_clists: "Card_order (clists r)"
       
   199 unfolding clists_def by (rule card_of_Card_order)
       
   200 
       
   201 lemma Cnotzero_clists: "Cnotzero (clists r)"
       
   202 by (simp add: clists_def card_of_ordIso_czero_iff_empty lists_not_empty)
       
   203 
       
   204 end
   186 end