reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;

theorem Th3:
  0 <= i0 implies i0 in NAT
proof
  consider k such that
A1: i0 = k or i0 = - k by Th2;
  assume 0 <= i0;
  then i0 = - k implies i0 is Element of NAT;
  hence thesis by A1, ORDINAL1:def 12;
end;
