fact: Definition quotient_lower_set_bottom (pX : bottom_element RX) : bottom_element quotient_lower_set.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets