src/HOL/Finite_Set.thy
changeset 27418 564117b58d73
parent 27165 e1c49eb8cee6
child 27430 1e25ac05cd87
equal deleted inserted replaced
27417:6cc897e2468a 27418:564117b58d73
   253   apply (erule finite_subset, assumption)
   253   apply (erule finite_subset, assumption)
   254   done
   254   done
   255 
   255 
   256 lemma finite_range_imageI:
   256 lemma finite_range_imageI:
   257     "finite (range g) ==> finite (range (%x. f (g x)))"
   257     "finite (range g) ==> finite (range (%x. f (g x)))"
   258   apply (drule finite_imageI, simp)
   258   apply (drule finite_imageI, simp add: range_composition)
   259   done
   259   done
   260 
   260 
   261 lemma finite_imageD: "finite (f`A) ==> inj_on f A ==> finite A"
   261 lemma finite_imageD: "finite (f`A) ==> inj_on f A ==> finite A"
   262 proof -
   262 proof -
   263   have aux: "!!A. finite (A - {}) = finite A" by simp
   263   have aux: "!!A. finite (A - {}) = finite A" by simp