refactor(RingTheory/Ideal/Height): torwards private Ideal.primeHeight

[Thmoas-Guan]

---

• depends on: refactor(RingTheory/Ideal/Heoght): minimize usages of Ideal.primeHeight and add lemma for minimalPrimes #37500

[github-actions]

PR summary 6ef8cc2731

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ Ideal.height_add_one_le_of_lt_of_isPrime
+ Ideal.height_eq_inf_minimalPrimes
+ Ideal.height_eq_order_height_of_isPrime
+ Ideal.height_eq_ringKrullDim_iff
+ Ideal.height_eq_zero_iff
+ Ideal.height_le_ringKrullDim_of_isPrime
+ Ideal.height_lt_top_of_isPrime
+ Ideal.height_mono_of_isPrime
+ Ideal.height_ne_top_of_isPrime
+ Ideal.height_strict_mono_of_isPrime
+ Ideal.height_strict_mono_of_isPrime_of_isPrime
+ Ideal.isMaximal_of_height_eq_ringKrullDim
+ Ideal.le_minimalPrimes
+ Ideal.sup_height_isPrime_eq_ringKrullDim
+ Ideal.sup_height_of_maximal_eq_ringKrullDim
+ IsLocalization.height_comap_eq_of_isPrime
+ minimalPrimes_isPrime
- Ideal.height_strict_mono_of_is_prime

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./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).

[mathlib-dependent-issues]

This PR/issue depends on:

• refactor(RingTheory/Ideal/Heoght): minimize usages of Ideal.primeHeight and add lemma for minimalPrimes #37500
  By Dependent Issues (🤖). Happy coding!