reserve n for Nat,
  a,b for Real,
  s for Real_Sequence;

theorem
  for n being Real holds (n+1)|^3=n|^3+3*n|^2+3*n+1 & (n+1)|^4=n
|^4+4*n|^3+6*n|^2+4*n+1 & (n+1)|^5=n|^5+5*n|^4+10*n|^3+10*n|^2+5*n+1 by Lm4,Lm6
