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feat(RingTheory/Polynomial): some lemmas about Ideal.leadingCoeff#37336

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mbkybky:leadingCoeff
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feat(RingTheory/Polynomial): some lemmas about Ideal.leadingCoeff#37336
mbkybky wants to merge 2 commits intoleanprover-community:masterfrom
mbkybky:leadingCoeff

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@mbkybky mbkybky commented Mar 29, 2026

Add some lemmas about Ideal.leadingCoeff.


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github-actions bot commented Mar 29, 2026

PR summary 56e100aabd

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ leadingCoeff_finset_prod_le
+ leadingCoeff_mono
+ leadingCoeff_mul_le
+ leadingCoeff_pow_le
+ leadingCoeff_top
+ map_C_comap_of_comap_eq_leadingCoeff
+ map_C_leadingCoeff

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).

@github-actions github-actions bot added the t-ring-theory Ring theory label Mar 29, 2026
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github-actions bot commented Mar 29, 2026

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

@mbkybky mbkybky changed the title feat(RingTheory/Polynomial) : some lemmas about Ideal.leadingCoeff feat(RingTheory/Polynomial): some lemmas about Ideal.leadingCoeff Mar 29, 2026
@@ -493,6 +494,44 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
⟨i + j, I.leadingCoeffNth_mono (Nat.le_add_right _ _),
I.leadingCoeffNth_mono (Nat.le_add_left _ _)⟩

lemma leadingCoeff_mono {I J : Ideal R[X]} (hIJ : I ≤ J) : I.leadingCoeff ≤ J.leadingCoeff := by
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Suggested change
lemma leadingCoeff_mono {I J : Ideal R[X]} (hIJ : I ≤ J) : I.leadingCoeff ≤ J.leadingCoeff := by
@[gcongr]
lemma leadingCoeff_mono {I J : Ideal R[X]} (hIJ : I ≤ J) : I.leadingCoeff ≤ J.leadingCoeff := by

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