$\forall$${\it es}$:ES, $A$:Type, $X$:AbsInterface($A$ List), ${\it e'}$, $e$:E.
\\[0ex]$e$ $\leq$loc ${\it e'}$  $\Rightarrow$ es{-}interface{-}history(${\it es}$;$X$;$e$) $\leq$ es{-}interface{-}history(${\it es}$;$X$;${\it e'}$)