reserve x,y,Y,Z for set,
  L for LATTICE,
  l for Element of L;

theorem Th24:
  for L being LATTICE, l being Element of L st l is prime holds l
  is irreducible
proof
  let L be LATTICE, l be Element of L;
  assume
A1: l is prime;
  let x,y be Element of L;
  assume
A2: l = x "/\" y;
  then x "/\" y <= l;
  then
A3: x <= l or y <= l by A1;
  l <= x & l <= y by A2,YELLOW_0:23;
  hence thesis by A3,ORDERS_2:2;
end;
