reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem
  n > 0 implies 2 to_power(n) is even
proof
  assume n > 0;
  then 2 to_power(n) mod 2 = 0 by NAT_2:17;
  hence thesis by NAT_2:21;
end;
