Section curry_compose.
Context {a b c : C}.

(** composing with curry is equivalent to compose and then curry: *)
Lemma curry_compose (f : ((×ᶠⁿᶜ C) _o (a, b))%object –≻ c)
{z : C} (g : z –≻ a)
: (curry f) ∘ g = curry (f ∘ (Prod_morph_ex _ _ (g ∘ Pi_1) Pi_2)).