(* The explicit value of the inverse is needed for the proof of the second    *)
(* orthogonality relation.                                                    *)
Let XX'_1: X *m X' = 1%:M.

Lemma eq_irr_mem_classP x y :
y \in G -> reflect (forall i, 'chi[G]_i x = 'chi_i y) (x \in y ^: G).