 If formula_12 and formula_13 then formula_14.For all "a", "b", "x", and "y" in a Riesz space "X", we have "a" - inf("x", "y") + b = sup("a" - "x" + "b", "a" - "y" + "b").For every element "x" in a Riesz space "X", the absolute value of "x", denoted by formula_15, is defined to be formula_16, where this satisfies -|"x"| ≤ "x" ≤ |"x"| and |"x"| ≥ 0.