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Guidelines when cleaning up traits #1338

@prabau

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@prabau

What should the guidelines be when cleaning up traits for a space?

On the one hand, it is logically pleasing to have a minimal set of asserted traits. It also reduces clutter in the list of the asserted traits for a space. And it has also become easier for us to detect redundant traits, as pi-base conveniently gives an indication by displaying the alternate derivation if the trait were not asserted.

On the other hand, some traits that have a simple justification can be derived from other traits in a much more complicated way.

For an instructive example, see #1334 or #1337. P22 (pseudocompact) is true for the irrational numbers with an immediate justification (https://topology.pi-base.org/spaces/S000028/properties/P000022). Looking at the S28-cleanup branch from #1337, the same property has an automated full derivation using 13 theorems, some of which are highly non-trivial. Or the fact that the irrationals have cardinality of the continuum (P65) can be derived in 24 steps.

So what should be the pi-base guidelines when cleaning up traits for pi-base? Do we go for deep cleaning or shallow cleaning?

Anyone involved in pi-base, please share your opinion.
(pinging @StevenClontz @ccaruvana if you don't have automatic notification)

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