I believe that the "tree of life" contained the unique ingredients that Adam & Eve needed in order to sustain their lives forever. I also believe that they were at least periodically eating from this tree, for the reason that the other tree was the only one of the two that was off-grounds for them. It was only AFTER they disobeyed that they were prevented from eating of the tree of life any longer. Had they not disobeyed it appears that they would have continued to live for as long as they replenished the needs of their bodies by consuming the essential ingredients that could be found in the tree of life alone.
No question about it, they had permission to eat of the tree of life.
The fruit from the tree of life really had life-sustaining ingredients.
The fruit from the "other" tree was simply good for food, just plain ole food, and to eat from it was to disobey God and merit not being worthy of eating of the tree of life any longer.
So Adam and Eve would still be alive today had they not been disallowed from eating from the tree of life.
We die for the same reason that Adam and Eve died ... because we need the ingredients from the tree of life and aren't getting them.
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