Definition irrType := socleType aG.
Identity Coercion type_of_irrType : irrType >-> socleType.
Variable sG : irrType.
Definition irr_degree (i : sG) := \rank (socle_base i).
Local Notation "'n_ i" := (irr_degree i) : group_ring_scope.
Local Open Scope group_ring_scope.

(* Specifications: *)
Lemma irr_degreeE i : 'n_i = \rank (socle_base i). Proof. by []. Qed.
Lemma irr_degree_gt0 i : 'n_i > 0.
Lemma principal_comp_subproof : mxsimple aG (rfix_mx aG G).
Fact principal_comp_key : unit. Proof. by []. Qed.