feat(PrimeSpectrum): clopens in spectra of CommSemirings

[alreadydone]

We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements (e,f) such that e * f = 0 and e + f = 1. This happens precisely when ![e,f] is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.

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[github-actions]

PR summary 77deafe50b

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Ring.Idempotents	160	161	+1 (+0.62%)

Import changes for all files

Files	Import difference
Mathlib.Algebra.Ring.Idempotents	1

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Declarations diff

+ basicOpen_eq_zeroLocus_of_mul_add
+ iff_eq_one_of_isUnit
+ isClopen_iff_mul_add
+ isClopen_iff_mul_add_zeroLocus
+ mulZeroaddOneEquivClopens
+ of_mul_add
+ zeroLocus_eq_basicOpen_of_mul_add

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).