Here's mine: Wikipedia: Anthropic Principle
Strong anthropic principle (SAP): "The Universe must have those properties which allow life to develop within it at some stage in its history."
Final anthropic principle (FAP): "Intelligent information-processing must come into existence in the Universe, and, once it comes into existence, it will never die out."
they take on values restricted . That is backwards. They don't take on values. They are values.
As to the proof: It is not faith if the proof is possible, even if the philosophy prof marks up the paper so it bleeds.