
theorem Th34:
  for L being LATTICE for p being Element of L st p is prime holds
  p is pseudoprime
proof
  let L be LATTICE, p be Element of L;
  assume p is prime;
  then
A1: downarrow p is prime by Th33;
  p = sup downarrow p by WAYBEL_0:34;
  hence ex P being prime Ideal of L st p = sup P by A1;
end;
