reserve L for Lattice,
  p,q,r for Element of L,
  p9,q9,r9 for Element of L.:,
  x, y for set;
reserve I,J for Ideal of L,
  F for Filter of L;
reserve D for non empty Subset of L,
  D9 for non empty Subset of L.:;
reserve D1,D2 for non empty Subset of L,
  D19,D29 for non empty Subset of L.:;

theorem
  (.I \/ J.> = (.I "\/" J.>
proof
A1: (.I"\/"J.> = <.(I"\/"J).:.) by Th36;
  (.I \/ J.> = <.(I \/ J).:.) & I.:"/\"J.: = I"\/"J by Th36,Th44;
  hence thesis by A1,FILTER_0:37;
end;
