You mean competition between cells in a multi-cellular organism? They don't compete, they come from the same DNA and they "win" by perpetuating that DNA, not their own self. Your cells are not subject to evolution -- you are, as a whole.
Doesn't this line of reasoning prove the non-existence of cancer?
No, I don't think so. Cancerous cells don't win at evolution. In fact, is they manage to kill the host, they explicitly lose.
Survival of the fittest doesn't prove the non-existence of broken bones, either.
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