[Merged by Bors] - chore(data/fin): succ_above defn compares fin terms instead of values #3999
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Co-authored-by: Shing Tak Lam <shingtaklam1324@gmail.com>
This change makes quadratic_reciprocity compile again, likely. The lemma could probably have norm_cast attr.
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Co-authored by: Bryan Gin-ge Chen bryangingechen@gmail.com
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…#3999) `fin.succ_above` is redefined to use a comparison between two `fin (n + 1)` instead of their coerced values in `nat`. This should delay any "escape" from `fin` into `nat` until necessary. Lemmas are added regarding `fin.succ_above`. Some proofs for existing lemmas reworked for new definition and simplified. Additionally, docstrings are added for related lemmas. New lemmas: Comparison after embedding: `succ_above_lt_ge` `succ_above_lt_gt` Injectivity lemmas: `succ_above_right_inj` `succ_above_right_injective` `succ_above_left_inj` `succ_above_left_injective` finset lemma: `fin.univ_succ_above` prod and sum lemmas: `fin.prod_univ_succ_above` Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
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…#3999) `fin.succ_above` is redefined to use a comparison between two `fin (n + 1)` instead of their coerced values in `nat`. This should delay any "escape" from `fin` into `nat` until necessary. Lemmas are added regarding `fin.succ_above`. Some proofs for existing lemmas reworked for new definition and simplified. Additionally, docstrings are added for related lemmas. New lemmas: Comparison after embedding: `succ_above_lt_ge` `succ_above_lt_gt` Injectivity lemmas: `succ_above_right_inj` `succ_above_right_injective` `succ_above_left_inj` `succ_above_left_injective` finset lemma: `fin.univ_succ_above` prod and sum lemmas: `fin.prod_univ_succ_above` Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
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fin.succ_aboveis redefined to use a comparison between twofin (n + 1)instead of their coerced values innat. This should delay any "escape" fromfinintonatuntil necessary. Lemmas are added regardingfin.succ_above. Some proofs for existing lemmas reworked for new definition and simplified. Additionally, docstrings are added for related lemmas.New lemmas:
Comparison after embedding:
succ_above_lt_gesucc_above_lt_gtInjectivity lemmas:
succ_above_right_injsucc_above_right_injectivesucc_above_left_injsucc_above_left_injectivefinset lemma:
fin.univ_succ_aboveprod and sum lemmas:
fin.prod_univ_succ_aboveI'm working on some statements like
It seems that generalization might make the
fin.prod_*lemmas generalizable over genericfinset.eraseprodlemmas. Is it worth it to express them in that general way? In particular, due to howfin nandfin (n + 1)are different types, rearranging indices (that usefinas the type) within those sums gets clunky. Hopefully the generalizations will ease that clunkiness.