reserve L for Lattice,
  p,p1,q,q1,r,r1 for Element of L;
reserve x,y,z,X,Y,Z,X1,X2 for set;
reserve H,F for Filter of L;
reserve D for non empty Subset of L;
reserve D1,D2 for non empty Subset of L;

theorem Th22:
  D1 c= D2 implies <.D1.) c= <.D2.)
proof
  assume
A1: D1 c= D2;
  D2 c= <.D2.) by Def4;
  then D1 c= <.D2.) by A1;
  hence thesis by Def4;
end;
