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[Merged by Bors] - feat(linear_algebra/direct_sum): submodule_is_internal_iff_independent_and_supr_eq_top#9214
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eric-wieser wants to merge 26 commits intomasterfrom
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[Merged by Bors] - feat(linear_algebra/direct_sum): submodule_is_internal_iff_independent_and_supr_eq_top#9214eric-wieser wants to merge 26 commits intomasterfrom
submodule_is_internal_iff_independent_and_supr_eq_top#9214eric-wieser wants to merge 26 commits intomasterfrom
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Also golf some uses of `quotient.lift_on` to use `quotient.map`.
…uotient.lift_on`" This reverts commit 7f136ef.
complete_lattice.independent_iff_dfinsupp_lsum_kersubmodule_is_internal_iff_independent_and_supr_eq_top
…p-injective-independent
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eric-wieser
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Sep 25, 2021
eric-wieser
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Sep 30, 2021
kim-em
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Oct 1, 2021
kim-em
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Oct 1, 2021
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bors d+ |
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✌️ eric-wieser can now approve this pull request. To approve and merge a pull request, simply reply with |
jcommelin
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Oct 1, 2021
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>
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Thanks 🎉 bors merge |
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I'm a little puzzled by bors here. This PR has the label "awaiting-CI" but bors did not reject it. As far as I know bors uses the configuration from the master branch, which indeed contains: |
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Perhaps bors won't reject it until it hits the top of the queue? |
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Ah, I misremembered! From the docs
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…nt_and_supr_eq_top` (#9214) This shows that a grade decomposition into submodules is bijective iff and only iff the submodules are independent and span the whole module. The key proofs are: * `complete_lattice.independent_of_dfinsupp_lsum_injective` * `complete_lattice.independent.dfinsupp_lsum_injective` Everything else is just glue. This replaces parts of #8246, and uses what is probably a similar proof strategy, but without unfolding down to finsets. Unlike the proof there, this requires only `add_comm_monoid` for the `complete_lattice.independent_of_dfinsupp_lsum_injective` direction of the proof. I was not able to find a proof of `complete_lattice.independent.dfinsupp_lsum_injective` with the same weak assumptions, as it is not true! A counter-example is included, Co-authored-by: Hanting Zhang <hantingzhang03@gmail.com>
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Pull request successfully merged into master. Build succeeded: |
submodule_is_internal_iff_independent_and_supr_eq_topsubmodule_is_internal_iff_independent_and_supr_eq_top
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This shows that a grade decomposition into submodules is bijective iff and only iff the submodules are independent and span the whole module.
The key proofs are:
complete_lattice.independent_of_dfinsupp_lsum_injectivecomplete_lattice.independent.dfinsupp_lsum_injectiveEverything else is just glue.
This replaces parts of #8246, and uses what is probably a similar proof strategy, but without unfolding down to finsets.
Unlike the proof there, this requires only
add_comm_monoidfor thecomplete_lattice.independent_of_dfinsupp_lsum_injectivedirection of the proof. I was not able to find a proof ofcomplete_lattice.independent.dfinsupp_lsum_injectivewith the same weak assumptions, as it is not true! A counter-example is included,Co-authored-by: Hanting Zhang hantingzhang03@gmail.com
filter_ne_eq_erase#9182