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[Merged by Bors] - feat(algebra/*,group_theory/*): instances/lemmas about is_scalar_tower and smul_comm_class #9533

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[Merged by Bors] - feat(algebra/*,group_theory/*): instances/lemmas about is_scalar_tower and smul_comm_class #9533

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@urkud urkud commented Oct 4, 2021

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@urkud urkud 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 4, 2021
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Update src/group_theory/group_action/prod.lean
38fcc5e 
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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src/group_theory/group_action/prod.lean
Comment on lines +49 to +53
@[to_additive]
instance smul_comm_class_both [monoid N] [monoid P] [has_scalar M N] [has_scalar M P]
[smul_comm_class M N N] [smul_comm_class M P P] :
smul_comm_class M (N × P) (N × P) :=
⟨λ c x y, by simp [smul_def, mul_def, mul_smul_comm]⟩
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Strictly we should also have the

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@[to_additive]
instance smul_comm_class_both [monoid N] [monoid P] [has_scalar M N] [has_scalar M P]
[smul_comm_class M N N] [smul_comm_class M P P] :
smul_comm_class M (N × P) (N × P) :=
⟨λ c x y, by simp [smul_def, mul_def, mul_smul_comm]⟩
@[to_additive]
instance smul_comm_class_both' [monoid N] [monoid P] [has_scalar M N] [has_scalar M P]
[smul_comm_class N M N] [smul_comm_class P M P] :
smul_comm_class (N × P) M (N × P) :=
sorry

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I prefer to add instances as we need them.

@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 9, 2021
@urkud urkud requested a review from eric-wieser October 9, 2021 21:11
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bors d+

Two nits, but feel free to merge as is if you don't care about them.

src/algebra/opposites.lean
instance _root_.smul_comm_class.opposite_mid {M N} [monoid N] [has_scalar M N]
[is_scalar_tower M N N] :
smul_comm_class M Nᵒᵖ N :=
⟨λ x y z, by { induction y using opposite.op_induction, simp [smul_mul_assoc] }⟩
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I suspect this has a much shorter term mode proof, but not worth spending much time on.

src/group_theory/group_action/defs.lean
lemma is_scalar_tower.of_smul_one_mul {M N} [monoid N] [has_scalar M N]
(h : ∀ (x : M) (y : N), (x • (1 : N)) * y = x • y) :
is_scalar_tower M N N :=
⟨λ x y z, by rw [← h, smul_eq_mul, mul_assoc, h, smul_eq_mul]⟩
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If we had a is_scalar_tower.of_smul_mul_assoc then this proof probably becomes shorter.

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✌️ urkud can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@github-actions github-actions bot added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels Oct 10, 2021
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urkud commented Oct 10, 2021

bors merge

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Oct 10, 2021
bors bot pushed a commit that referenced this pull request Oct 10, 2021
@urkud @eric-wieser
feat(algebra/*,group_theory/*): instances/lemmas about `is_scalar_tow…
897a3b1 
…er` and `smul_comm_class` (#9533)




Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Build failed (retrying...):

bors bot pushed a commit that referenced this pull request Oct 10, 2021
@urkud @eric-wieser
feat(algebra/*,group_theory/*): instances/lemmas about `is_scalar_tow…
fa41436 
…er` and `smul_comm_class` (#9533)




Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Pull request successfully merged into master.

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@bors bors bot changed the title feat(algebra/*,group_theory/*): instances/lemmas about is_scalar_tower and smul_comm_class [Merged by Bors] - feat(algebra/*,group_theory/*): instances/lemmas about is_scalar_tower and smul_comm_class Oct 10, 2021
@bors bors bot closed this Oct 10, 2021
@bors bors bot deleted the extra-instances branch October 10, 2021 23:32
@eric-wieser eric-wieser added the hacktoberfest-accepted Without this label hacktoberfest is scared off by bors label Oct 12, 2021
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