Arguments aut_Iirr_inj {gT G} u [i1 i2] : rename.
Arguments conjC_IirrK {gT G} i : rename.
Section Coset.
Variable (gT : finGroupType).
Implicit Types G H : {group gT}.

(* Specifications: *)
Lemma cfQuo_char G H (chi : 'CF(G)) :
chi \is a character -> (chi / H)%CF \is a character.
Lemma cfQuo_lin_char G H (chi : 'CF(G)) :
chi \is a linear_char -> (chi / H)%CF \is a linear_char.
Lemma quo_IirrK G H i :
H <| G -> H \subset cfker 'chi[G]_i -> mod_Iirr (quo_Iirr H i) = i.
Lemma quo_IirrKeq G H :
H <| G ->
forall i, (mod_Iirr (quo_Iirr H i) == i) = (H \subset cfker 'chi[G]_i).
Lemma mod_Iirr_bij H G :
H <| G -> {on [pred i | H \subset cfker 'chi_i], bijective (@mod_Iirr G H)}.
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.
Lemma cap_cfker_normal G H :
H <| G -> \bigcap_(i | H \subset cfker 'chi[G]_i) (cfker 'chi_i) = H.
Lemma cfker_reg_quo G H : H <| G -> cfker (cfReg (G / H)%g %% H) = H.
End Coset.