reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem
  for k being Integer holds 2*k+1, 9*k+4 are_coprime
  proof
    let k be Integer;
    thus (2*k + 1) gcd (9*k + 4) = (2*k + 1) gcd ((9*k + 4) - 4*(2*k + 1))
    by NEWTON02:5
    .= 1 gcd k by NEWTON02:5
    .= 1;
  end;
