Quaeritur: Are deductive demonstration and inductive demonstration equivalent to saying “a fortiori” and “a posteriori” demonstration respectively? God bless.
Respondeo: You probably mean "a priori" and "a posteriori." The answer is: not necessarily. A priori and a posteriori can be used in different senses.
One sense is: prior to experience and posterior to experience. For example, prior to experience (or a priori), I know that all the bachellors that you are friends with are unmarried. I don't need to meet them and interview them to know they are unmarried. But I can only know a posteriori (after meeting them), that such and such a bachellor, who is your friend, is six feet tall or has a Canadian accent, or whatever. This is the most common meaning assigned to this word pair among today's scholars because it is the sense in which Kant used the word pair. In this sense, induction is always a posteriori (because it necessarily proceeds from particulars, which are known through experience), whereas deduction can be a priori, but is not always.
But there is a second sense of a priori and a posteriori which is applicable to deduction: deduction a priori or "from the prior" (i.e., from the cause), or deduction a posteriori "from the posterior" (i.e., from the effect)--more technical terms for this distinction are: propter quid demonstration vs. quia demonstration. For example, suppose they say that the International Space Station will be visible tonight where you live. They say it will look the size of your average star, and its angular distance will be much faster than that of a star (but much slower than a shooting star), such that it will take about a minute to cross the night sky. But you wonder whether it will twinkle like the stars or not. You reason in the following way: any heavenly body that is relatively near, compared to the stars, does not twinkle, because what causes a heavenly body to twinkle is its enormous distance from Earth (the light from objects that are far is more susceptible to being altered by the Earth's atmosphere, which causes the twinkling). So you conclude that the Space Station will not twinkle, because it is relatively near, compared to the stars. In essence, your reasoning proceeds from a premise that has to do with the cause (being near), to a conclusion that relates to the effect (not twinkling). This is deductive a priori reasoning, or a propter quid demonstration.
But, alternately, suppose that you are looking at a heavenly object at night, and you notice it does not twinkle. You reason that it must be relatively near to Earth (like a planet), because it does not twinkle. Your reasoning proceeds from a premise that has to do with the effect (not twinkling) to a conclusion that relates to the cause (being near). This is deductive a posteriori reasoning, or a quia demonstration. This is the sense in which many Thomists and translators of St. Thomas use the terms a priori and a posteriori. I prefer simply to use the Latin: quia and propter quid demonstrations. Aristotle (and Aquinas in his Commentary) go into detail concerning these two kinds of demonstration in the Posterior Analytics.