equal
deleted
inserted
replaced
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" |