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
  poly_diff(p-q) = poly_diff(p) - poly_diff(q)
  proof
    thus poly_diff(p-q) = poly_diff(p) + poly_diff(-q) by Th47
    .= poly_diff(p) - poly_diff(q) by Th48;
  end;
