The growing practice of using proof assistant software to create and mechanically check formal proofs of challenging mathematical results relies crucially on the prior formalisation of their elementary prerequisites. These include both common undergraduate material and mundane, essentially trivial facts about symbol manipulation. The feasibility of bigger proofs depends, sometimes critically, on how one has chosen to formalise these « little theories ». This talk will explore some instances of such dependencies, drawn from my experience in formalising the proofs of the Four Colour and Odd Order theorems.
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