Definition cfDprodl := cfSdprod (dprodWsdC KxH).
Definition cfDprod phi psi := cfDprodl phi * cfDprodr psi.
Canonical cfDprodl_additive := [additive of cfDprodl].
Canonical cfDprodl_linear := [linear of cfDprodl].
Canonical cfDprodl_rmorphism := [rmorphism of cfDprodl].
Canonical cfDprodl_lrmorphism := [lrmorphism of cfDprodl].
Canonical cfDprodr_additive := [additive of cfDprodr].
Canonical cfDprodr_linear := [linear of cfDprodr].
Canonical cfDprodr_rmorphism := [rmorphism of cfDprodr].
Canonical cfDprodr_lrmorphism := [lrmorphism of cfDprodr].

Lemma cfdot_dprod phi1 phi2 psi1 psi2 :
'[cfDprod phi1 psi1, cfDprod phi2 psi2] = '[phi1, phi2] * '[psi1, psi2].