Total Preorder

A total preorder is a Preorder where any two elements are comparable. Has properties:

• $\forall x,y,z\text{ if }x\lesssim y\wedge y\lesssim z⟹x\lesssim z$ (Transitive)
• $\forall x,y,x\lesssim y\vee y\lesssim x$ (Reflexive)