: (_ x); rewrite -[irr_degree _]natCK -irr1_degree lin_char1 //.
by rewrite (natCK 1) => A; rewrite trace_mx11 -mx11_scalar.
Qed.Fact linear_char_key B : pred_key (@linear_char B). Pite invr_lin_char // qualifE cfunE.
by rewrite rpredM ?lin_char1 ?mulr1 ?lin_charW //= cfConjC_lin_char.
Qed.Section OrthogonalityRelations.DprodC. Qed.ite mulrA mulfK ?irr1_neq0 // => <-; congr (_ * _).
by apply: eq_bigr => x; rewrite mulg1.
Qed.

(* The character table. *)Definition irr_class i := enum_val (cast_ord (NirrE G) i).Local Notation c := irr_class.

(* Specifications: *)
Proof. by case/repr_classesP: (