
theorem Th33:
  for L being LATTICE, p being Element of L st p is prime holds
  downarrow p is prime
proof
  let L be LATTICE, p be Element of L such that
A1: for x,y being Element of L st x"/\"y <= p holds x <= p or y <= p;
  let x,y be Element of L;
  assume x"/\"y in downarrow p;
  then x"/\"y <= p by WAYBEL_0:17;
  then x <= p or y <= p by A1;
  hence thesis by WAYBEL_0:17;
end;
