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_exp_prod2: forall A prod expo {ND : NatDed A} {CCC: CCCviaNatDed A prod expo} B P (Q: B -> A), prod P (exp Q) = exp (fun x => prod P (Q x)).