Sin entering into the world

Genesis 2:17 17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

Now, did it only mean that Adam died to his body? no, there had to be a redemption taking place, a lamb was killed in his stead to pay for Adams and Eves sin so to speak. If it was only bodily death no redemption would have been needed, now would it?

Romans 5:12 12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:

Now, it says that sin entered "into" the world by Adam, or does it really? Kosmos is the allready functionning world system, with people, that can only be said after Adam and Eve began to have children, and they having children too. It does not say that sin entered into the place called earth by one man, if that was true, how could the snake make Eve to sin and eat of the fruit of knowledge?

Now, as we can see from that, sin existed allready before Adam and Eve sinned against God, why else would they be prohibited from eating of the tree of knowledge if they could not be tempted to sin?

Where did sin enter into earth then? through lucifers rebellion against God.