reserve D,D9 for non empty set;
reserve R for Ring;
reserve G,H,S for non empty ModuleStr over R;
reserve UN for Universe;
reserve R for Ring;
reserve G, H for LeftMod of R;
reserve G1, G2, G3 for LeftMod of R;
reserve f for LModMorphismStr over R;

theorem Th20:
  for u being Element of UN holds succ u is Element of UN
proof
  let u be Element of UN;
  succ u = u \/ {u};
  hence thesis;
end;
