fact: Definition equiv_path_O_prod {X Y : Type} {x0 x1 : X} {y0 y1 : Y} : (to O _ (x0, y0) = to O _ (x1, y1)) <~> (to O _ x0 = to O _ x1) * (to O _ y0 = to O _ y1).
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout