Kosher Parve and/0r Vegan = Casein Free?

Before you read the following - please know that just because a product says Vegan or Kosher Parve - it does not guarantee that they are casein free with regard to a serious allergy.  I would, however, trust them with a casein sensitivity until proven otherwise (possible cross contamination).

I came across this randomly yesterday..  I know that Vegan usually means that a food is safe and free of Casein.  But now i can add Kosher Pareve / Kosher Parve to my list!

So, as I stumbled onto this strange symbol "Kp"  on a box  I began researching. I am a professional "digger".  Thanks to a college friend (who knows exactly who she is!) I am now  a "bunny trail-er" a.k.a. one who finds themselves wandering off the beaten path. I used to heckle her for constantly getting off path. Now I'm right there with her :)

Back to the story at hand... here is some basic info about Kp:

"The Jewish laws of kashrut (koshering) demand a number of dietary restrictions. For our purposes, the wonderful thing about kashrut is that milk and meat may not commingle. Therefore, kosher foods fall into three categories:

MILK: products which contain dairy or dairy derivatives or are processed on equipment which has processed dairy-containing products,

MEAT: products which contain meat or meat derivatives or are processed on equipment which has processed meat-containing products,

PAREVE: products which contain neither meat nor dairy, nor their derivatives, nor are produced on equipment which has processed meat or dairy products.