feat(RingTheory): Ideal.span corollaries of Krull's height theorem

[vlad902]

Currently we have statements bounding the height of minimal primes of Ideal.span S. Add the obvious corollaries to bound the height of Ideal.span S directly.

Also add a Set.encard-valued statement of Krull's height theorem. In a Noetherian ring we know the bound should always be finite, but this is useful in downstream applications that are using ENat.

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[github-actions]

PR summary a53dcb7feb

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

+ Ideal.height_le_encard_of_mem_minimalPrimes_span
+ Ideal.height_le_ncard_of_mem_minimalPrimes_span
+ Ideal.height_span_le_card_of_span_ne_top
+ Ideal.height_span_le_encard_of_span_ne_top
+ Ideal.height_span_le_ncard_of_span_ne_top

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit a53dcb7).

• +5 new declarations
• −0 removed declarations

+Ideal.height_le_encard_of_mem_minimalPrimes_span
+Ideal.height_le_ncard_of_mem_minimalPrimes_span
+Ideal.height_span_le_card_of_span_ne_top
+Ideal.height_span_le_encard_of_span_ne_top
+Ideal.height_span_le_ncard_of_span_ne_top

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit a53dcb7feb
Reference commit 85ce110e6b

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).

[robin-carlier]

The only question I’d have is whether or not we should just add the Set + Finite version and drop the Finset ones. Otherwise, LGTM.

[robin-carlier]

Thanks!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by robin-carlier.