equal
deleted
inserted
replaced
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 |