Section CfDotOrthonormal.
Variables (M : {group gT}) (S : seq 'CF(G)) (nu : 'CF(G) -> 'CF(M)).
Hypotheses (Inu : {in 'Z[S] &, isometry nu}) (onS : orthonormal S).
Let oSS := orthonormal_orthogonal onS.
Let freeS := orthogonal_free oSS.
Let nS1 : {in S, forall phi, '[phi] = 1}.
End CfDotOrthonormal.

Lemma vchar_norm2 phi :
phi \in 'Z[irr G, G^#] -> '[phi] = 2%:R ->
exists i, exists2 j, j != i & phi = 'chi_i - 'chi_j.