theorem
  L1 is B_Lattice & L2 is B_Lattice iff [:L1,L2:] is B_Lattice
proof
A1: [:L1,L2:] is D_Lattice iff L1 is D_Lattice & L2 is D_Lattice by Th38;
  [:L1,L2:] is C_Lattice iff L1 is C_Lattice & L2 is C_Lattice by Th45;
  hence thesis by A1;
end;
