src/HOL/Finite_Set.thy
changeset 54148 c8cc5ab4a863
parent 54147 97a8ff4e4ac9
child 54413 88a036a95967
equal deleted inserted replaced
54147:97a8ff4e4ac9 54148:c8cc5ab4a863
  1186 
  1186 
  1187 lemma card_ge_0_finite:
  1187 lemma card_ge_0_finite:
  1188   "card A > 0 \<Longrightarrow> finite A"
  1188   "card A > 0 \<Longrightarrow> finite A"
  1189   by (rule ccontr) simp
  1189   by (rule ccontr) simp
  1190 
  1190 
  1191 lemma card_0_eq [simp, no_atp]:
  1191 lemma card_0_eq [simp]:
  1192   "finite A \<Longrightarrow> card A = 0 \<longleftrightarrow> A = {}"
  1192   "finite A \<Longrightarrow> card A = 0 \<longleftrightarrow> A = {}"
  1193   by (auto dest: mk_disjoint_insert)
  1193   by (auto dest: mk_disjoint_insert)
  1194 
  1194 
  1195 lemma finite_UNIV_card_ge_0:
  1195 lemma finite_UNIV_card_ge_0:
  1196   "finite (UNIV :: 'a set) \<Longrightarrow> card (UNIV :: 'a set) > 0"
  1196   "finite (UNIV :: 'a set) \<Longrightarrow> card (UNIV :: 'a set) > 0"