fact: Definition prod_coind_uncurried `{A : X -> Type} `{B : X -> Type} : (forall x, A x) * (forall x, B x) -> (forall x, A x * B x) := fun fg x => (fst fg x, snd fg x).
imports: Basics.Overture Basics.Equivalences Basics.PathGroupoids Basics.Tactics Basics.Trunc Basics.Decidable Types.Empty