[abruzzi]

Definitions can absolutely be a priori. Think of the definition of a triangle, some thing like "a closed geometrical shape with three sides." There is nothing about observation of the world that will tell you that this is or isn't true. It is true by definition. Then all closed three sided shapes are triangles, by definition. Then you can start building all sorts of proofs from that, and a few other definitions. You get to the Pythagorean theorem, trigonometry, and off you go, without ever needing anything other than the ideas and definitions.