Fernando - I agree with what you're saying, however there's no clear link between sin=death and the fruit itself. God's threat to Adam and Eve that they would die was carried out, but only because they were denied further access to the Tree of Life. The death of Adam and Eve was therefore a punitive measure taken by God by depriving them of the remedy, i.e. the eternal life granted by the tree of life. It was like denying an asthmatic person his inhaler during an attack (if you'll excuse the morbid analogy).
Some have said they hadn't yet eaten from the tree of life before they were banished, but I find that hard to believe when reviewing the context of the narrative. Adam and Eve were encouraged to eat from every tree of the garden (including the tree of life) excluding only the tree of knowledge - why would they abstain from it prior to the events leading to their banishment?
Paul's writings seem to super-impose the concept of inherited sin over the narrative, and imbue the forbidden fruit with some mystical death-dealing properties (not referred to in Genesis) that would transcend generations for which Christ's redeeming blood was required. Yes, God said "in the day you eat from it you will die" but that didn't happen - they died hundreds of years later. And there was nothing in God's warning to suggest that the fruit itself would deliver the deathblow, purely that there would be fatal consequences to the act of disobedience.
If you take away Paul's letters, that is not what is described in Genesis. What is described is God more-or-less saying "you can't have the best of both worlds", and banishing them from the garden to stop them from becoming godlike, i.e. having both eternal life, and wisdom.
Cedars