fact: Definition O_prod_cmp_coind (A B : Type) : O_prod_cmp A B == prod_coind (O_rec (to O _ o fst : A * B -> O A)) (O_rec (to O _ o snd : A * B -> O B)) := O_rec_functor_prod _ _.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout