[Coq-Club] [Agda] Re: [HoTT] newbie questions about homotopy theory & advantage of UF/Coq

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Thu Jan 9 11:18:52 CET 2014

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==


More information about the Agda mailing list