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From: | Slawomir Kolodynski |
Subject: | Re: [Isarmathlib-devel] A contribution |
Date: | Sat, 8 Sep 2012 10:37:39 -0700 (PDT) |
>the case of the partitions Partitions_ZF theory contains some as-hoc tools that were needed for some particular proof. If some other definitions suite you better, go ahead. > in the context real0 and real1 there is mistake Good catch, thanks. One thing that I don't like in your metric space development is that you use the real1 locale. This locale is used for the construction of a particular model or real numbers. The construction allows to claim that there exist quadruplets of sets that satisfy the predicate IsAmodelOfReals(K,A,M,r). However, there is no reason to restrict the definition of metric to this particular model of reals. I would prefer the approach where we put an assumption in a locale that IsAmodelOfReals(K,A,M,r) and that is your set of real numbers, without any specifics. This is how it is done Complex_ZF.thy's locale complex0. Another thing you might want to consider is (not) putting assumptions in definitions. To be honest I didn't know this is even possible in Isabelle. I see one good reason to do it: standard mathematicians do it. Every definition in standard math starts with some assumptions that set the context for which this definitions is intended to be used. However, not having the premises in definitions allows more flexibility in the contexts you can use it. The definition of metric is a good example. It would be interesting to see how far one can go assuming that metrics are valued in an ordered field (without assuming the least upper bound property that would make it a model of reals). If you move your assumptions to theorems (from definitions) you can show exactly what you can prove without the least upper bound property and where this property plays a role. Please treat the above as my opinions only. The rule number one is that who does the work decides how it should be done. Slawekk --- On Sat, 9/8/12, daniel <address@hidden> wrote:
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