
theorem N0344:
  for a,b be non weightless Integer holds a,b are_coprime implies
    not a divides b & not b divides a
  proof
    let a,b be non weightless Integer;
    assume
    A1: a,b are_coprime;
    |.a.| in NAT by INT_1:3; then
    reconsider x = |.a.| as non trivial Nat;
    |.b.| in NAT by INT_1:3; then
    reconsider y = |.b.| as non trivial Nat;
    x,y are_coprime by A1,INT_2:34; then
    not x divides y & not y divides x by NEWTON03:44;
    hence thesis by INT_2:16;
  end;
