
theorem
  for L be non empty RelStr for x be Element of L holds x in PRIME (L
  opp) iff x is co-prime
proof
  let L be non empty RelStr;
  let x be Element of L;
  hereby
    assume x in PRIME (L opp);
    then x~ in PRIME (L opp) by LATTICE3:def 6;
    then x~ is prime by WAYBEL_6:def 7;
    hence x is co-prime by WAYBEL_6:def 8;
  end;
  assume x is co-prime;
  then x~ is prime by WAYBEL_6:def 8;
  then x~ in PRIME (L opp) by WAYBEL_6:def 7;
  hence thesis by LATTICE3:def 6;
end;
