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[Merged by Bors] - feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + algebra_map #9829

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[Merged by Bors] - feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + algebra_map #9829

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Vierkantor
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Some simp lemmas I needed for combining algebra_map with ideal.quotient.mk. This also allowed me to golf two existing proofs.

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@Vierkantor Vierkantor added 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. labels Oct 20, 2021
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Vierkantor commented Oct 20, 2021
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src/ring_theory/ideal/operations.lean
Comment on lines +1476 to +1482
@[simp] lemma quotient.mk_comp_algebra_map (I : ideal A) :
(quotient.mk I).comp (algebra_map R A) = algebra_map R I.quotient :=
rfl

@[simp] lemma quotient.mk_algebra_map (I : ideal A) (x : R) :
quotient.mk I (algebra_map R A x) = algebra_map R I.quotient x :=
rfl
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I chose for simp to go in this direction for these two lemmas since it makes working with alg_homs a bit easier, and the RHS is shorter. Flipping the direction is also fine with me, since there are quite a few ideal.quotient.mk-specific lemmas in this file.

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Are we missing an alg_hom.commute_of_tower lemma or something to make it less annoying to have these in the other direction?

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If I understand your question correctly, they do exist, as alg_hom.map_algebra_map and alg_hom.comp_algebra_map_of_tower. The issue is that quotient.mk is only a ring_hom, not an alg_hom, so we need to reprove all the algebra_map-related things anyway.

@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 Oct 20, 2021
@Vierkantor Vierkantor mentioned this pull request Oct 21, 2021
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jcommelin approved these changes Oct 23, 2021
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Thanks 🎉

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 Oct 23, 2021
bors bot pushed a commit that referenced this pull request Oct 23, 2021
@Vierkantor
feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + `alg…
5436bf9 
…ebra_map` (#9829)

Some `simp` lemmas I needed for combining `algebra_map` with `ideal.quotient.mk`. This also allowed me to golf two existing proofs.
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bors r+

bors bot pushed a commit that referenced this pull request Oct 23, 2021
@Vierkantor
feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + `alg…
0411b1e 
…ebra_map` (#9829)

Some `simp` lemmas I needed for combining `algebra_map` with `ideal.quotient.mk`. This also allowed me to golf two existing proofs.
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bors bot commented Oct 23, 2021

Pull request successfully merged into master.

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@bors bors bot changed the title feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + algebra_map [Merged by Bors] - feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + algebra_map Oct 23, 2021
@bors bors bot closed this Oct 23, 2021
@bors bors bot deleted the ideal-quotient-algebra_map_eq branch October 23, 2021 19:26
@eric-wieser eric-wieser added the hacktoberfest-accepted Without this label hacktoberfest is scared off by bors label Oct 26, 2021
ericrbg pushed a commit that referenced this pull request Nov 9, 2021
@Vierkantor @ericrbg
feat(ring_theory/ideal): simp lemmas for ideal.quotient.mk + `alg…
77debb2 
…ebra_map` (#9829)

Some `simp` lemmas I needed for combining `algebra_map` with `ideal.quotient.mk`. This also allowed me to golf two existing proofs.
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