src/HOL/Algebra/Complete_Lattice.thy
changeset 67399 eab6ce8368fa
parent 67340 150d40a25622
child 68488 dfbd80c3d180
equal deleted inserted replaced
67398:5eb932e604a2 67399:eab6ce8368fa
  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