[Merged by Bors] - feat(order/locally_finite): introduce locally finite orders #9464
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The new typeclass `locally_finite_order` homogeneizes treatment of intervals as `finset`s and `multiset`s. `finset.Ico` is now available for all locally finite orders (instead of being ℕ-specialized), rendering `finset.Ico_ℤ` and `pnat.Ico` useless. This PR also introduces the long-awaited `finset.Icc`, `finset.Ioc`, `finset.Ioo`, and `finset.Ici`, `finset.Ioi` (for `order_top`s) and `finset.Iic`, `finset.Iio` (for `order_bot`s), and the `multiset` variations thereof.
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The new typeclass
locally_finite_orderhomogeneizes treatment of intervals asfinsets andmultisets.finset.Icois now available for all locally finite orders (instead of being ℕ-specialized), renderingfinset.Ico_ℤandpnat.Icouseless.This PR also introduces the long-awaited
finset.Icc,finset.Ioc,finset.Ioo, andfinset.Ici,finset.Ioi(fororder_tops) andfinset.Iic,finset.Iio(fororder_bots), and themultisetvariations thereof.I haven't redefined
finset.Icoandmultiset.Icoin this PR to avoid needing to change all the API. #7987 will take care offinset.Icoand another PR will follow formultiset.Ico.Another PR (reviving the branch fin_range) about intervals as ordered lists will hopefully follow. This is strictly less general than what we have here as many
locally_finite_orders are nonlinear.