fact: Definition functor_prod {A A' B B' : Type} (f:A->A') (g:B->B') : A * B -> A' * B' := fun z => (f (fst z), g (snd z)).
imports: Basics.Overture Basics.Equivalences Basics.PathGroupoids Basics.Tactics Basics.Trunc Basics.Decidable Types.Empty