[Merged by Bors] - feat(group_theory/nilpotent): add antimono and functorial lemma for lower central series #8853
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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| lemma lower_central_series_antimono (n : ℕ) : | ||
| lower_central_series G n.succ ≤ lower_central_series G n := |
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Could you please generalise this to m \le n, instead of merely n \le n.succ. That will be more useful in practice.
(There must be a suitable induction lemma somewhere in mathlib that reduces the general statement to the current version in 1 or 2 lines.)
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We have monotone_nat_of_le_succ but we need to apply this to the opposite lattice :-/ . How about defining antitone and antitone_nat_of_succ_le? Or maybe using the opposite lattice is fine if you keep your head.
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I think it shouldn't be too hard to apply it to order_dual nat.
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This looks fine to me now. |
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…ower central series (#8853) Co-authored-by: ineswright <52750254+ineswright@users.noreply.github.com>
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…ower central series (#8853) Co-authored-by: ineswright <52750254+ineswright@users.noreply.github.com>
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Note that the more general lemma descending_central_series_antimono I believe is not provable from the current definition of descending central series.