[Merged by Bors] - chore(Data/Nat/Factorial): Use Std lemmas #11715
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Move basic `Nat` lemmas from `Data.Nat.Order.Basic` and `Data.Nat.Pow` to `Data.Nat.Defs`. Most proofs need adapting, but that's easily solved by replacing the general mathlib lemmas by the new Std `Nat`-specific lemmas and using `omega`.
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Make use of `Nat`-specific lemmas from Std rather than the general ones provided by mathlib. The ultimate goal here is to carve out `Data`, `Algebra` and `Order` sublibraries.
eric-wieser
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| lemma monotone_factorial : Monotone factorial := fun _ _ => factorial_le | ||
| #align nat.monotone_factorial Nat.monotone_factorial | ||
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Surely this doesn't belong in this file?
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There's already stuff about orders in there and I don't really feel like creating a new file just for this one lemma. I'm not quite sure where Monotone will stand in the upcoming sublibraries but I think it will be in Order and not imported by Nat.factorial.
I'm happy for you to open a PR creating that Data.Nat.Factorial.Order file if you want though, or maybe it can be in Data.Nat.Order.Lemmas. Up to you.
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| tendsto_atTop_atTop_of_monotone Nat.monotone_factorial fun n ↦ ⟨n, n.self_le_factorial⟩ | ||
| tendsto_atTop_atTop_of_monotone (fun _ _ ↦ Nat.factorial_le) fun n ↦ ⟨n, n.self_le_factorial⟩ |
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I would have thought you should just import monotone_factorial here; it's very weird to consider Tendsto more elementary than Monotone IMO.
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Yeah sorry, that's an accident. I had originally put monotone_factorial in Data.Nat.Factorial.Cast, so I didn't put to import it in Analysis.SpecificLimits.Basic.
Louddy
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Make use of `Nat`-specific lemmas from Std rather than the general ones provided by mathlib. The ultimate goal here is to carve out `Data`, `Algebra` and `Order` sublibraries.
atarnoam
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Make use of `Nat`-specific lemmas from Std rather than the general ones provided by mathlib. The ultimate goal here is to carve out `Data`, `Algebra` and `Order` sublibraries.
uniwuni
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Make use of `Nat`-specific lemmas from Std rather than the general ones provided by mathlib. The ultimate goal here is to carve out `Data`, `Algebra` and `Order` sublibraries.
callesonne
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Make use of `Nat`-specific lemmas from Std rather than the general ones provided by mathlib. The ultimate goal here is to carve out `Data`, `Algebra` and `Order` sublibraries.
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Make use of
Nat-specific lemmas from Std rather than the general ones provided by mathlib.The ultimate goal here is to carve out
Data,AlgebraandOrdersublibraries.