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;

theorem Th19:
  (ex r st p "/\" r <> p) implies <.p.) <> the carrier of L
proof
  given r such that
A1: p "/\" r <> p;
  p "/\" r [= p by LATTICES:6;
  then not p [= p "/\" r by A1,LATTICES:8;
  hence thesis by Th15;
end;
