reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  k>0 & x divides a+k & x divides a-k implies x <= 2*k
  proof
    assume
    A1: k>0;
    x divides a+k & x divides a-k implies x divides 2*a & x divides 2*k
      by Th22;
    hence thesis by A1,NAT_D:7;
  end;
