Definition irr_constt (B : {set gT}) phi := [pred i | '[phi, 'chi_i]_B != 0].

(* Specifications: *)
Lemma irr_consttE i phi : (i \in irr_constt phi) = ('[phi, 'chi_i]_G != 0).
Lemma cfun_sum_constt (phi : 'CF(G)) :
phi = \sum_(i in irr_constt phi) '[phi, 'chi_i] *: 'chi_i.
Lemma neq0_has_constt (phi : 'CF(G)) :
phi != 0 -> exists i, i \in irr_constt phi.
Lemma constt_irr i : irr_constt 'chi[G]_i =i pred1 i.
Lemma char1_ge_constt (i : Iirr G) chi :
chi \is a character -> i \in irr_constt chi -> 'chi_i 1%g <= chi 1%g.
Lemma constt_ortho_char (phi psi : 'CF(G)) i j :
phi \is a character -> psi \is a character ->
i \in irr_constt phi -> j \in irr_constt psi ->
'[phi, psi] = 0 -> '['chi_i, 'chi_j] = 0.