src/HOL/Finite_Set.thy
changeset 40702 cf26dd7395e4
parent 40311 994e784ca17a
child 40703 d1fc454d6735
equal deleted inserted replaced
40683:a3f37b3d303a 40702:cf26dd7395e4
  2284 apply simp
  2284 apply simp
  2285 done
  2285 done
  2286 
  2286 
  2287 lemma finite_UNIV_surj_inj: fixes f :: "'a \<Rightarrow> 'a"
  2287 lemma finite_UNIV_surj_inj: fixes f :: "'a \<Rightarrow> 'a"
  2288 shows "finite(UNIV:: 'a set) \<Longrightarrow> surj f \<Longrightarrow> inj f"
  2288 shows "finite(UNIV:: 'a set) \<Longrightarrow> surj f \<Longrightarrow> inj f"
  2289 by (blast intro: finite_surj_inj subset_UNIV dest:surj_range)
  2289 by (blast intro: finite_surj_inj subset_UNIV)
  2290 
  2290 
  2291 lemma finite_UNIV_inj_surj: fixes f :: "'a \<Rightarrow> 'a"
  2291 lemma finite_UNIV_inj_surj: fixes f :: "'a \<Rightarrow> 'a"
  2292 shows "finite(UNIV:: 'a set) \<Longrightarrow> inj f \<Longrightarrow> surj f"
  2292 shows "finite(UNIV:: 'a set) \<Longrightarrow> inj f \<Longrightarrow> surj f"
  2293 by(fastsimp simp:surj_def dest!: endo_inj_surj)
  2293 by(fastsimp simp:surj_def dest!: endo_inj_surj)
  2294 
  2294