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It's crazy to think that we didn't really know for sure whether 1+1=2 until ~1910, yet it's true. That's when Bernard Russell (best known for Russell's teapot, exposing a logical fallacy in Christianity) and some other dude actually proved it from axioms. They laid out the foundation of 1+1 in a book called Principia Mathematica. They worked so rigorously that it took them 360 pages to even prove something as basic as 1+1=2 using the axiomatic method. If you want to use a modern tool like Coq to verify 1+1=2, then the best way of doing this is to formalize Principia Mathematica in Coq.
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