equal
deleted
inserted
replaced
1169 subsection \<open>Examples\<close> |
1169 subsection \<open>Examples\<close> |
1170 |
1170 |
1171 subsubsection \<open>The Powerset of a Set is a Complete Lattice\<close> |
1171 subsubsection \<open>The Powerset of a Set is a Complete Lattice\<close> |
1172 |
1172 |
1173 theorem powerset_is_complete_lattice: |
1173 theorem powerset_is_complete_lattice: |
1174 "complete_lattice \<lparr>carrier = Pow A, eq = op =, le = (op \<subseteq>)\<rparr>" |
1174 "complete_lattice \<lparr>carrier = Pow A, eq = (=), le = (\<subseteq>)\<rparr>" |
1175 (is "complete_lattice ?L") |
1175 (is "complete_lattice ?L") |
1176 proof (rule partial_order.complete_latticeI) |
1176 proof (rule partial_order.complete_latticeI) |
1177 show "partial_order ?L" |
1177 show "partial_order ?L" |
1178 by standard auto |
1178 by standard auto |
1179 next |
1179 next |