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[Merged by Bors] - feat(group_theory/index): Index of finite intersection #16393

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[Merged by Bors] - feat(group_theory/index): Index of finite intersection #16393

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@tb65536 tb65536 commented Sep 5, 2022 •
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This PR proves that the index of a finite intersection is at most the product of the indices.

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@tb65536 tb65536 added awaiting-review The author would like community review of the PR t-algebra Algebra (groups, rings, fields etc) labels Sep 5, 2022
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alreadydone commented Sep 9, 2022 •
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Is the proof via injectivity (from the coset space of the inf to the product of coset spaces) easier than the current inductive proof?

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tb65536 commented Sep 9, 2022

Is the proof via injectivity (from the coset space of the inf to the product of coset spaces) easier than the current inductive proof?

A little. And beefing up the coset space API seems useful.

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I didn't check but is the API somewhat parallel to the API leading up to ideal.quotient_inf_to_pi_quotient?

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tb65536 commented Sep 9, 2022

I didn't check but is the API somewhat parallel to the API leading up to ideal.quotient_inf_to_pi_quotient?

The main piece of API seems to be pi.ring_hom, but that sort of construction isn't helpful here.

@tb65536 tb65536 mentioned this pull request Sep 19, 2022
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@mathlib-dependent-issues-bot mathlib-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Sep 20, 2022
bors bot pushed a commit that referenced this pull request Sep 20, 2022
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feat(group_theory/coset): Construct the embedding `H ⧸ ⨅ i, f i → Π i…
a5ed408 
…, H ⧸ f i` (#16560)

This PR constructs the embedding `H ⧸ ⨅ i, f i  → Π i, H ⧸ f i`, which is needed for #16393.



Co-authored-by: Thomas Browning <tb65536@users.noreply.github.com>
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Sep 20, 2022
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This PR/issue depends on:

b-mehta pushed a commit that referenced this pull request Sep 21, 2022
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feat(group_theory/coset): Construct the embedding `H ⧸ ⨅ i, f i → Π i…
92d019a 
…, H ⧸ f i` (#16560)

This PR constructs the embedding `H ⧸ ⨅ i, f i  → Π i, H ⧸ f i`, which is needed for #16393.



Co-authored-by: Thomas Browning <tb65536@users.noreply.github.com>
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riccardobrasca approved these changes Oct 3, 2022
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Thanks!

bors d+

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bors bot commented Oct 3, 2022

✌️ tb65536 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@leanprover-community-bot-assistant leanprover-community-bot-assistant 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 3, 2022
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tb65536 commented Oct 4, 2022

bors r+

bors bot pushed a commit that referenced this pull request Oct 4, 2022
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feat(group_theory/index): Index of finite intersection (#16393)
a1b96f8 
This PR proves that the index of a finite intersection is at most the product of the indices.
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bors bot commented Oct 4, 2022

Pull request successfully merged into master.

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@bors bors bot changed the title feat(group_theory/index): Index of finite intersection [Merged by Bors] - feat(group_theory/index): Index of finite intersection Oct 4, 2022
@bors bors bot closed this Oct 4, 2022
@bors bors bot deleted the index_infi_le branch October 4, 2022 03:15
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