Fingernails are a very complex and specific mutation which only occurs in primates. Every animal with fingernails is a subset of primates. The subset of primates with fingernails and the specific mutation preventing a tail are called apes. Every animal with fingernails and no tail is an ape.
This is 4th grade math, it is called set theory and if an isolated species of lizard had the same specific complex mutation for fingernails - then the tree of life/evolution would violate set theory, but there is no such example in all of nature. If an isolated mammal had the specific mutation for feathers, that would violate set theory. If an isolated bird had the specific mutation for teets, that would violate set theory. If a fish had the specific mutation for hair, that would violate set theory.
Evolution conforms to set theory in exact detail - we all arise as a subset of genes which pattern indicates a single ancestor in specific detail. Either then evolution is a fact, or set theory is completely wrong and math itself is a farce.
http://en.wikipedia.org/wiki/Set_theory
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