fact: Definition equiv_O_prod_cmp (A B : Type) : O (A * B) <~> (O A * O B) := Build_Equiv _ _ (O_prod_cmp A B) _.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout