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[Merged by Bors] - feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas #18056

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[Merged by Bors] - feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas #18056

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@Multramate Multramate added easy < 20s of review time. See the lifecycle page for guidelines. awaiting-review The author would like community review of the PR awaiting-CI The author would like to see what CI has to say before doing more work. t-algebra Algebra (groups, rings, fields etc) labels Jan 3, 2023
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label Jan 4, 2023
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alreadydone approved these changes Jan 7, 2023
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Thanks 🎉

maintainer merge

src/ring_theory/ideal/operations.lean
@@ -443,6 +443,31 @@ lemma span_singleton_mul_le_span_singleton_mul {x y : R} {I J : ideal R} :
span {x} * I ≤ span {y} * J ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zI = y * zJ :=
by simp only [span_singleton_mul_le_iff, mem_span_singleton_mul, eq_comm]

lemma span_singleton_mul_right_mono [is_domain R] {x : R} (hx : x ≠ 0) :
span {x} * I ≤ span {x} * J ↔ I ≤ J :=
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One advantage of using submodule.pointwise_distrib_mul_action is that it doesn't require the semiring to be commutative, while ideal.has_mul requires it and hence doesn't allow you to state the noncommutative version. But let's not worry about that now.

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🚀 Pull request has been placed on the maintainer queue by alreadydone.

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github-actions bot commented Jan 7, 2023

🚀 Pull request has been placed on the maintainer queue by alreadydone.

@alreadydone alreadydone mentioned this pull request Jan 8, 2023
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ocfnash commented Jan 9, 2023

Thanks!

bors mege

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ocfnash commented Jan 9, 2023

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Jan 9, 2023
bors bot pushed a commit that referenced this pull request Jan 9, 2023
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feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas (
d13d624 
#18056)
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Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Jan 9, 2023
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feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas (
ba2d8fb 
#18056)
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bors bot commented Jan 9, 2023

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas [Merged by Bors] - feat(ring_theory/ideal/operations): add span_singleton_mul_left lemmas Jan 9, 2023
@bors bors bot closed this Jan 9, 2023
@bors bors bot deleted the ideal.span_singleton branch January 9, 2023 13:14
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