fact: Definition equiv_prod_coind `(A : X -> Type) (B : X -> Type) : ((forall x, A x) * (forall x, B x)) <~> (forall x, A x * B x) := Build_Equiv _ _ (@prod_coind_uncurried X A B) _.
imports: Basics.Overture Basics.Equivalences Basics.PathGroupoids Basics.Tactics Basics.Trunc Basics.Decidable Types.Empty