Based on https://en.wikipedia.org/wiki/Lattice_(order) should Lattice have the following additional laws?

• Supremum:
  • x || y >= x
  • x || y >= y
• Infimum:
  • x && y <= x
  • x && y <= y

We could potentially go even further and require that x || y is the least upper bound of {x, y}, and similar for &&.