feat(RingTheory/MvPolynomial/MonomialOrder): add leadingTerm lemmas

[NoahW314]

Add lemmas for leadingTerm to match those for leadingCoeff.

---

[github-actions]

PR summary d7282a6883

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ leadingTerm_X
+ leadingTerm_add_of_lt
+ leadingTerm_mul_of_isRegular_left
+ leadingTerm_mul_of_isRegular_right
+ leadingTerm_mul_of_left_mem_nonZeroDivisors
+ leadingTerm_mul_of_mul_leadingCoeff_ne_zero
+ leadingTerm_mul_of_right_mem_nonZeroDivisors
+ leadingTerm_neg
+ leadingTerm_one
+ leadingTerm_pow
+ leadingTerm_pow_of_pow_leadingCoeff_ne_zero
+ leadingTerm_prod_of_mem_nonZeroDivisors
+ leadingTerm_prod_of_regular
+ leadingTerm_sub_of_lt
+ leadingTerm_subsingleton

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 d7282a6).

• +15 new declarations
• −0 removed declarations

+MonomialOrder.leadingTerm_X
+MonomialOrder.leadingTerm_add_of_lt
+MonomialOrder.leadingTerm_mul_of_isRegular_left
+MonomialOrder.leadingTerm_mul_of_isRegular_right
+MonomialOrder.leadingTerm_mul_of_left_mem_nonZeroDivisors
+MonomialOrder.leadingTerm_mul_of_mul_leadingCoeff_ne_zero
+MonomialOrder.leadingTerm_mul_of_right_mem_nonZeroDivisors
+MonomialOrder.leadingTerm_neg
+MonomialOrder.leadingTerm_one
+MonomialOrder.leadingTerm_pow
+MonomialOrder.leadingTerm_pow_of_pow_leadingCoeff_ne_zero
+MonomialOrder.leadingTerm_prod_of_mem_nonZeroDivisors
+MonomialOrder.leadingTerm_prod_of_regular
+MonomialOrder.leadingTerm_sub_of_lt
+MonomialOrder.leadingTerm_subsingleton

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit d7282a6883
Reference commit 843d7890de

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).

[Hagb]

LGTM.
Maybe R⁰ is the preferred spelling of nonZeroDivisors R, I think, because it was suggested to replace nonZeroDivisors R with R⁰ in previous review in #34758.

[NoahW314]

Good to know. Thanks!