2![rewrite -irr_sum_square (mulr_suml, mulr_sumr); apply: eq_bigr => ? _].
  by rewrite dprod_IirrE -exprMn -{3}(mulg1 1%g) cfDprodE.
rewrite (eq_bigl _ _ Df) pair_bigA addrC -subr_eq0 addrK

(* Specifications: *)
Qed.