Notation xcfun_r A := (xcfun_r_head tt A).
Notation "phi .[ A ]" := (xcfun phi A) : cfun_scope.
Definition pred_Nirr gT B := #|@classes gT B|.-1.
Arguments pred_Nirr {gT} B%g.
Notation Nirr G := (pred_Nirr G).+1.
Notation Iirr G := 'I_(Nirr G).
Section IrrClassDef.
Variables (gT : finGroupType) (G : {group gT}).
Let sG := DecSocleType (regular_repr algCF G).

(* Specifications: *)
Lemma NirrE : Nirr G = #|classes G|.
Lemma irr0 : 'chi[G]_0 = 1.
Lemma cfun1_irr : 1 \in irr G.
Let sG := DecSocleType (regular_repr algCF G).