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 Th22:
  u divides t+z & u divides t-z implies u divides 2*t & u divides 2*z
  proof
A0: t + z = (t + t) + (z-t) & t + z = (t-z) + (z + z);
    assume
A1: u divides t+z & u divides t-z; then
    u divides -(t-z) by INT_2:10;
    hence thesis by A0,A1,INT_2:1;
  end;
