reserve L for D_Lattice;
reserve a, b, c for Element of L;
reserve L for B_Lattice;
reserve a, b for Element of L;

theorem
 for L being Lattice, S being initial final non empty Subset of L
   holds S = [#]L
 proof let L be Lattice, S be initial final non empty Subset of L;
   consider p being Element of L such that
A1:  p in S by SUBSET_1:4;
   for x being Element of L holds x in S iff x in [#]L
    proof let x be Element of L;
     thus x in S implies x in [#]L;
     assume x in [#]L;
A2:     x "/\" p in S by A1,Def22,Th4;
     thus x in S by A2,Def23,Th4;
    end;
  hence S = [#]L by SUBSET_1:3;
 end;
