reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;
reserve f,g for differentiable Function of REAL,REAL;
reserve L for non empty ZeroStr;
reserve x for Element of L;
reserve p,q for Polynomial of F_Real;

theorem Th45:
  p <> 0_.F_Real implies len p = len poly_diff(p) + 1
  proof
    assume p <> z;
    then len poly_diff(p) = len p - 1 by Th44;
    hence thesis;
  end;
