Did death occur before Adam and Eve´s sin?

Young earth creationists offen scuff at old earth creationists when they claim that millions of death occured, and therefore in response to that claim that Adam and Eve´s sin brought death to the animal kingdom also.

But we have to remember one thing. The animals did NOT eat of the tree of life, only Adam and Eve did that, so death did exist prior to the Adam and Eve eating of the tree of knowledge.

Genesis 2:9 9 And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil.

Only of the tree of knowledge werent they allowed, but the tree of life they was allowed to eat of. The tree of life was there to keep Adam and Eve from dieing.

Revelation 22:2 2 In the midst of the street of it, and on either side of the river, was there the tree of life, which bare twelve manner of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.

The tree of life will once more be available in the future, and for the same purpose.