The title can be a little unclear. But what I am basically saying is say we add a reactant to a reaction to push the reaction forward toward the product side, that reactant which was increased in amount/ concentration will surely less. Part of it used to produce more products to gain new equilibrium. But will it always be more than the original amount in the equilibrium before?
Without knowing much of advanced math, I just experimented with some simple fractions; thus far I haven't seen anything that violate this rule.