Definition principal_comp_def :=
PackSocle (component_socle sG principal_comp_subproof).
Definition principal_comp := locked_with principal_comp_key principal_comp_def.
Local Notation "1" := principal_comp : irrType_scope.

(* Specifications: *)
Lemma irr1_rfix : (1%irr :=: rfix_mx aG G)%MS.
Lemma rank_irr1 : \rank 1%irr = 1%N.
Lemma degree_irr1 : 'n_1 = 1%N.
Definition Wedderburn_subring (i : sG) := <<i *m R_G>>%MS.