Section Coset.
Variable (gT : finGroupType).
Implicit Types G H : {group gT}.

Lemma sum_norm_irr_quo H G x :
x \in G ->  H <| G ->
\sum_i `|'chi[G / H]_i (coset H x)| ^+ 2
= \sum_(i | H \subset cfker 'chi_i) `|'chi[G]_i x| ^+ 2.