reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;

theorem Th3:
  for a being natural Number holds a = 0 or a in Seg a
proof
  let a be natural Number;
  assume a <> 0;
  then ex b be Nat st a = b + 1 by NAT_1:6;
  then a in NAT & 1 <= a by NAT_1:11;
  hence thesis;
end;
