Class CCCviaNatDed (A: Type) (prod expo: A -> A -> A) {ND: NatDed A}: Prop :=
  isCCC: CartesianClosedCat.CCC A derives eq prod expo.Class CCCviaNatDed (A: Type) (prod expo: A -> A -> A) {ND: NatDed A}: Prop :=
  isCCC: CartesianClosedCat.CCC A derives eq prod expo.

Lemma CCC_prod_FF: forall A prod expo {ND : NatDed A} {CCC: CCCviaNatDed A prod expo} P, prod P FF = FF.