[frozen for bug reproduction] feat: integrate high-level order typeclasses with BEq and Ord
#9430
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OrderData with BEq and OrdBEq and Ord
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BEq and OrdBEq and Ord
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BEq and OrdBEq and Ord
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) This PR makes `IsPreorder`, `IsPartialOrder`, `IsLinearPreorder` and `IsLinearOrder` extend `BEq` and `Ord` as appropriate, adds the `LawfulOrderBEq` and `LawfulOrderOrd` typeclasses relating `BEq` and `Ord` to `LE`, and adds many lemmas and instances. Note: This PR contains a refactoring where `Init.Data.Ord` is moved to `Init.Data.Ord.Basic`. If I added `Init.Data.Ord` simply importing all submodules, git would not be able to determine that `Init.Data.Ord` was renamed to `Init.Data.Ord.Basic`. This could lead to unnecessary merge conflicts in the future. Hence, I chose the name `Init.Data.OrdRoot` instead of `Init.Data.Ord` temporarily. After this PR, I will rename this module back to `Init.Data.Ord` in a separate PR. (This is a copy of #9430: I will not touch that PR because it currently allows to debug a CI problem and pushing commits might break the reproducibility.)
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This PR makes
IsPreorder,IsPartialOrder,IsLinearPreorderandIsLinearOrderextendBEqandOrdas appropriate, adds theLawfulOrderBEqandLawfulOrderOrdtypeclasses relatingBEqandOrdtoLE, and adds many lemmas and instances.Note: This PR contains a refactoring where
Init.Data.Ordis moved toInit.Data.Ord.Basic. If I addedInit.Data.Ordsimply importing all submodules, git would not be able to determine thatInit.Data.Ordwas renamed toInit.Data.Ord.Basic. This could lead to unnecessary merge conflicts in the future. Hence, I chose the nameInit.Data.OrdRootinstead ofInit.Data.Ordtemporarily. After this PR, I will rename this module back toInit.Data.Ordin a separate PR.