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_prod1: forall A prod expo {ND : NatDed A} {CCC: CCCviaNatDed A prod expo} B (P: B -> A) Q, prod (exp P) Q = exp (fun x => prod (P x) Q).