fact: Definition subset_bounded_lattice : bounded_lattice (subtype_set X).
imports: UniMath.Foundations.Preamble UniMath.Foundations.PartA UniMath.Foundations.Sets UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Propositions UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.OrderTheory.Lattice.Lattice UniMath.OrderTheory.Lattice.Bounded UniMath.OrderTheory.Lattice.Distributive UniMath.OrderTheory.Lattice.Complement UniMath.OrderTheory.Lattice.Boolean