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.

Lemma degree_irr1 : 'n_1 = 1%N.
Definition Wedderburn_subring (i : sG) := <<i *m R_G>>%MS.