The answer is: deductive reasoning.
Deductive reasoning, colloquially known as top-down logic, does, indeed, move from a general statement to a specific case, although the movement is not as simple as that. More formally, deductive reasoning is a form of reasoning that logically links a set of premises in order to reach a certain conclusion; that is to say, if all premises are true and logical rules are applied, then the conclusion that is reached will, of logical necessity, be true, too.