[ refactor ] (more) decidable Data.Fin.Properties

[jamesmckinna]

This PR refactors some proofs about Decidable predicates on Fin n, to clarify some, and to add others, including some additional syntax, around a independently interesting minimisation principle from which certain others follow.

A downstream refactoring might reconsider these things in terms of specialisation of lemmas in Induction.InfiniteDescent.

Outstanding issue: could be more systematic about use of variables to clean the whole module up?

[jamesmckinna]

Thanks @MatthewDaggitt for the feedback:

• regarding lifting out these properties to a new module, that does seem like a good idea
• regarding naming/(use of) syntax, indeed there are lots of stylistic questions about the current version.

I'll move to DRAFT for the time being, and remove from v2.3, while I reconsider things.

[JacquesCarette]

All the code seems fine. Only issues are that things seem to have moved without a good reason to.

[jamesmckinna]

Hmmm... @JacquesCarette the code motion was in response to earlier review comments from @MatthewDaggitt , but maybe I misunderstood his intention. Nevertheless, the Quantification section is necessary for the subsequent decFinSubset and all?/any? definitions... so it seemed cognate to keep them together (esp. given the public re-export in Data.Fin.Properties...)

[JacquesCarette]

I had seen some of the conversation. This is why maybe a larger break up (Data.Fin.Properties.Quantification too?) might make more sense. Same with the Effectful stuff, it most definitely does not belong in .Properties.Decidable. The main code motion does make a lot of sense, it just has knock-on consequences.

[jamesmckinna]

Last addition: dual version of searchMin so that client use doesn't have to figure out the DNE...