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;
