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I'm working through Terence Tao's Real Analysis textbooks which start from Peano's axioms and build up from there and I was wondering can I use Coq to formalise and verify my proofs but without having to learn the existing libraries? I would like to start from scratch: enter the same axioms and then to refer only to them and to the previously proven statements in my proofs. The book uses set-theoretic framework.

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    $\begingroup$ that would be quite obscene in my opinion $\endgroup$ – Jorge Fernández Hidalgo Oct 25 '17 at 15:19

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