Variable i : Iirr G.
Let n := irr_degree (socle_of_Iirr i).
Let mxZn_inj: injective (@scalar_mx algCfield n).

(* A more usable reformulation that does not involve the class sums. *)
Corollary Aint_class_div_irr1 x :
x \in G -> #|x ^: G|%:R * 'chi_i x / 'chi_i 1%g \in Aint.