Canonical cfInd_linear := Linear cfInd_is_linear.
End Def.
Local Notation "''Ind[' B , A ]" := (@cfInd B A) : ring_scope.
Local Notation "''Ind[' B ]" := 'Ind[B, _] : ring_scope.

Lemma cfIndEsdprod (phi : 'CF(K)) x :
K ><| H = G -> 'Ind[G] phi x = \sum_(w in H) phi (x ^ w)%g.