reserve L for Lattice;
reserve X,Y,Z,V for Element of L;
reserve L for D_Lattice;
reserve X,Y,Z for Element of L;
reserve L for 0_Lattice;
reserve X,Y,Z for Element of L;

theorem Th14:
  X meets Y "/\" Z implies X meets Y & X meets Z
proof
  assume X meets Y "/\" Z;
  then
A1: X "/\" (Y "/\" Z) <> Bottom L;
  then X "/\" Z "/\" Y <> Bottom L by LATTICES:def 7;
  then
A2: X "/\" Z <> Bottom L;
  X "/\" Y "/\" Z <> Bottom L by A1,LATTICES:def 7;
  then X "/\" Y <> Bottom L;
  hence thesis by A2;
end;
