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;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem Th88:
  2 divides 2|^n - 1 iff n = 0
  proof
    L1: 2 divides 2|^n - 1 implies n = 0
    proof
      assume
      A1: not thesis; then
      2 divides 2|^n & not 2 divides -1 by NAT_3:3,INT_2:13;
      hence contradiction by A1;
    end;
    n = 0 implies 2|^n - 1 = 1 - 1 by NEWTON:4;
    hence thesis by INT_2:12,L1;
  end;
