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 Th11:
  u divides (u+z)|^n iff u divides z|^n
  proof
    A0: u divides (u+z)|^n - z|^n by Th10;
    consider t such that
    A1: t = - z|^n;
    A2: u divides (u+z)|^n + t by A0,A1; then
    A3: u divides t implies u divides (u+z)|^n by INT_2:1;
    u divides (u+z)|^n implies u divides t by INT_2:1,A2;
    hence thesis by A1,A3,INT_2:10;
  end;
