feat(data/fin*): uniqueness of increasing bijection #2258
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urkud
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bryangingechen
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Mar 29, 2020
| gives `(a + b)^n`. The "good" proof involves expanding along all coordinates using the fact that | ||
| `x^n` is multilinear, but multilinear maps are only available now over rings, so we give instead | ||
| a proof reducing to the usual binomial theorem to have a result over semirings. -/ | ||
| lemma fintype.sum_pow_mul_eq_add_pow |
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I did a bit of a refactor of this lemma yesterday. I first proved the lemma prod_add {α R : Type*} [comm_semiring R] (f g : α → R) (s : finset α) : s.prod (λ a, f a + g a) = s.powerset.sum (λ t : finset α, t.prod f * (s.filter (∉ t)).prod g) and restated this lemma using a finset α instead of the whole of α and finset.powerset in place of finset.univ, and proving it using prod_add. Are you happy for me to push these changes to this branch?
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
|
I made some changes. I'll let @urkud review my changes. |
urkud
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PR #2048 changed the CI so that olean caches are not pushed to Azure if a later commit on the same branch occurs. The reasoning was that it was unlikely that anyone would fetch those caches. That's changed as of #2278, since `fetch_olean_cache.sh` now looks for caches from commits earlier in the history. This means that currently, we can observe the following wasteful sequence of events in several PRs (e.g. #2258): 1. commit A gets pushed to a certain branch and CI_A starts. 2. While CI_A is still running the `leanpkg build` step, commit B is pushed and CI_B starts. 3. CI_A finishes `leanpkg build` but doesn't upload its cache to Azure because of #2048 4. Now commit C is pushed and can't use the results of CI_A 5. CI_B finishes `leanpkg build` but doesn't upload its cache 6. Commit D is pushed and can't use the results of CI_A or CI_B ... (This can keep happening as long as the next commit arrives before the most recent CI uploads to Azure). I also cleaned up some stuff that was left over from when we ran the build on both "pr" and "push" events.
anrddh
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May 15, 2020
…nity#2258) * feat(data/fin*): uniqueness of increasing bijection * protect * remove tidy call * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * prove prod_add, and use this to prove sum_pow_mul_eq_add_pow * forgot to save * fix build * remove card_sub_card Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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PR leanprover-community#2048 changed the CI so that olean caches are not pushed to Azure if a later commit on the same branch occurs. The reasoning was that it was unlikely that anyone would fetch those caches. That's changed as of leanprover-community#2278, since `fetch_olean_cache.sh` now looks for caches from commits earlier in the history. This means that currently, we can observe the following wasteful sequence of events in several PRs (e.g. leanprover-community#2258): 1. commit A gets pushed to a certain branch and CI_A starts. 2. While CI_A is still running the `leanpkg build` step, commit B is pushed and CI_B starts. 3. CI_A finishes `leanpkg build` but doesn't upload its cache to Azure because of leanprover-community#2048 4. Now commit C is pushed and can't use the results of CI_A 5. CI_B finishes `leanpkg build` but doesn't upload its cache 6. Commit D is pushed and can't use the results of CI_A or CI_B ... (This can keep happening as long as the next commit arrives before the most recent CI uploads to Azure). I also cleaned up some stuff that was left over from when we ran the build on both "pr" and "push" events.
anrddh
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May 16, 2020
…nity#2258) * feat(data/fin*): uniqueness of increasing bijection * protect * remove tidy call * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * prove prod_add, and use this to prove sum_pow_mul_eq_add_pow * forgot to save * fix build * remove card_sub_card Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
anrddh
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PR leanprover-community#2048 changed the CI so that olean caches are not pushed to Azure if a later commit on the same branch occurs. The reasoning was that it was unlikely that anyone would fetch those caches. That's changed as of leanprover-community#2278, since `fetch_olean_cache.sh` now looks for caches from commits earlier in the history. This means that currently, we can observe the following wasteful sequence of events in several PRs (e.g. leanprover-community#2258): 1. commit A gets pushed to a certain branch and CI_A starts. 2. While CI_A is still running the `leanpkg build` step, commit B is pushed and CI_B starts. 3. CI_A finishes `leanpkg build` but doesn't upload its cache to Azure because of leanprover-community#2048 4. Now commit C is pushed and can't use the results of CI_A 5. CI_B finishes `leanpkg build` but doesn't upload its cache 6. Commit D is pushed and can't use the results of CI_A or CI_B ... (This can keep happening as long as the next commit arrives before the most recent CI uploads to Azure). I also cleaned up some stuff that was left over from when we ran the build on both "pr" and "push" events.
cipher1024
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Mar 15, 2022
…nity#2258) * feat(data/fin*): uniqueness of increasing bijection * protect * remove tidy call * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/finset.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * Update src/data/fintype/card.lean Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com> * prove prod_add, and use this to prove sum_pow_mul_eq_add_pow * forgot to save * fix build * remove card_sub_card Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
cipher1024
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Mar 15, 2022
PR leanprover-community#2048 changed the CI so that olean caches are not pushed to Azure if a later commit on the same branch occurs. The reasoning was that it was unlikely that anyone would fetch those caches. That's changed as of leanprover-community#2278, since `fetch_olean_cache.sh` now looks for caches from commits earlier in the history. This means that currently, we can observe the following wasteful sequence of events in several PRs (e.g. leanprover-community#2258): 1. commit A gets pushed to a certain branch and CI_A starts. 2. While CI_A is still running the `leanpkg build` step, commit B is pushed and CI_B starts. 3. CI_A finishes `leanpkg build` but doesn't upload its cache to Azure because of leanprover-community#2048 4. Now commit C is pushed and can't use the results of CI_A 5. CI_B finishes `leanpkg build` but doesn't upload its cache 6. Commit D is pushed and can't use the results of CI_A or CI_B ... (This can keep happening as long as the next commit arrives before the most recent CI uploads to Azure). I also cleaned up some stuff that was left over from when we ran the build on both "pr" and "push" events.
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Additional material on the increasing bijection between
fin kand an ordered finset (uniqueness, and the fact that it maps0to the minimum of the set andk-1to its maximum), together with miscellaneous material on finsets and fintypes.