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 Th26:
  L is 0_Lattice & Bottom L in F implies F = <.L.) & F = the carrier of L
proof
  F = <.F.) by Th21;
  hence thesis by Th25;
end;
