Section CoproductLaws.
Context
{Equivalence_C : forall a b, @Equivalence (C a b) eq2}
{Category_C : Category C}
{Coproduct_C : Coproduct C bif}.
Global Instance Coproduct_sub : Coproduct sub sbif.

Lemma bimap_sub_unfold a b c d (f : sub a c) (g : sub b d) :
eq2 (C := C) (bimap (C := sub) f g)
(to_bif >>> bimap (C := C) f g >>> from_bif).