$\forall$$s$:QOSet, $a$, $b$, ${\it b'}$:$\mid$$s$$\mid$. ($b$ $<$$s$ ${\it b'}$) $\Rightarrow$ ($\uparrow$(($a$ $<_{b}$ $b$) $\Rightarrow_{b}$ ($a$ $<_{b}$ ${\it b'}$)))