src/HOL/ZF/HOLZF.thy
changeset 63901 4ce989e962e0
parent 63167 0909deb8059b
child 67443 3abf6a722518
equal deleted inserted replaced
63899:dc036b1a2a6f 63901:4ce989e962e0
   268 lemma Fun_total: "\<lbrakk>Elem F (Fun U V); Elem a U\<rbrakk> \<Longrightarrow> \<exists>x. Elem (Opair a x) F"
   268 lemma Fun_total: "\<lbrakk>Elem F (Fun U V); Elem a U\<rbrakk> \<Longrightarrow> \<exists>x. Elem (Opair a x) F"
   269   using [[simp_depth_limit = 2]]
   269   using [[simp_depth_limit = 2]]
   270   by (auto simp add: Fun_def Sep Domain)
   270   by (auto simp add: Fun_def Sep Domain)
   271 
   271 
   272 
   272 
   273 lemma unique_fun_value: "\<lbrakk>isFun f; Elem x (Domain f)\<rbrakk> \<Longrightarrow> ?! y. Elem (Opair x y) f"
   273 lemma unique_fun_value: "\<lbrakk>isFun f; Elem x (Domain f)\<rbrakk> \<Longrightarrow> \<exists>!y. Elem (Opair x y) f"
   274   by (auto simp add: Domain isFun_def)
   274   by (auto simp add: Domain isFun_def)
   275 
   275 
   276 lemma fun_value_in_range: "\<lbrakk>isFun f; Elem x (Domain f)\<rbrakk> \<Longrightarrow> Elem (f\<acute>x) (Range f)"
   276 lemma fun_value_in_range: "\<lbrakk>isFun f; Elem x (Domain f)\<rbrakk> \<Longrightarrow> Elem (f\<acute>x) (Range f)"
   277   apply (auto simp add: Range)
   277   apply (auto simp add: Range)
   278   apply (drule unique_fun_value)
   278   apply (drule unique_fun_value)