[Merged by Bors] - feat: NNRat.cast
#11203
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…atCast` Reduce the diff of #11203
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These lemmas are needed to define the semifield structure on `NNRat`, hence I am repurposing `Algebra.Order.Field.Defs` from avoiding a timeout (which I believe was solved long ago) to avoiding to import random stuff in the definition of the semifield structure on `NNRat` (although this PR doesn't actually reduce imports there, it will be in a later PR). Reduce the diff of #11203
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`Rat` has a long history in (and before) mathlib and as such its development is full of cruft. Now that `NNRat` is a thing, there is a need for the theory of `Rat` to be mimickable to yield the theory of `NNRat`, which is not currently the case. Broadly, this PR aims at mirroring the `Rat` and `NNRat` declarations. It achieves this by: * Relying more on `Rat.num` and `Rat.den`, and less on the structure representation of `Rat` * Abandoning the vestigial `Rat.Nonneg` (which was replaced in Std by a new development of the order on `Rat`) * Renaming many `Rat` lemmas with dubious names. This creates quite a lot of conflicts with Std lemmas, whose names are themselves dubious. I am priming the relevant new mathlib names and leaving TODOs to fix the Std names. * Handling most of the `Rat` porting notes Reduce the diff of #11203
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This is the parts of the diff of #11203 which don't mention `NNRat.cast`. * Use more `where` notation. * Write `qsmul := _` instead of `qsmul := qsmulRec _`. * Move `qsmul` before `ratCast_def` in instance declarations. * Name more instances. * Rename `rat_smul` to `qsmul`. *
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This is the parts of the diff of #11203 which don't mention `NNRat.cast`. * Use more `where` notation. * Write `qsmul := _` instead of `qsmul := qsmulRec _` to make the instances more robust to definition changes. * Delete `qsmulRec`. * Move `qsmul` before `ratCast_def` in instance declarations. * Name more instances. * Rename `rat_smul` to `qsmul`.
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Code looks fine, assuming this is a change we want.
maintainer merge
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
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NNRat.castNNRat.cast
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`Rat` has a long history in (and before) mathlib and as such its development is full of cruft. Now that `NNRat` is a thing, there is a need for the theory of `Rat` to be mimickable to yield the theory of `NNRat`, which is not currently the case. Broadly, this PR aims at mirroring the `Rat` and `NNRat` declarations. It achieves this by: * Relying more on `Rat.num` and `Rat.den`, and less on the structure representation of `Rat` * Abandoning the vestigial `Rat.Nonneg` (which was replaced in Std by a new development of the order on `Rat`) * Renaming many `Rat` lemmas with dubious names. This creates quite a lot of conflicts with Std lemmas, whose names are themselves dubious. I am priming the relevant new mathlib names and leaving TODOs to fix the Std names. * Handling most of the `Rat` porting notes Reduce the diff of #11203
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This is the parts of the diff of #11203 which don't mention `NNRat.cast`. * Use more `where` notation. * Write `qsmul := _` instead of `qsmul := qsmulRec _` to make the instances more robust to definition changes. * Delete `qsmulRec`. * Move `qsmul` before `ratCast_def` in instance declarations. * Name more instances. * Rename `rat_smul` to `qsmul`.
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This is the parts of the diff of #11203 which don't mention `NNRat.cast`. * Use more `where` notation. * Write `qsmul := _` instead of `qsmul := qsmulRec _` to make the instances more robust to definition changes. * Delete `qsmulRec`. * Move `qsmul` before `ratCast_def` in instance declarations. * Name more instances. * Rename `rat_smul` to `qsmul`.
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Define the canonical coercion from the nonnegative rationals to any division semiring.
From LeanAPAP
GroupWithZero#11202MulOpposite/AddOpposite#11485nat_cast/int_cast/rat_casttonatCast/intCast/ratCast#11486coe_nat/coe_int/coe_rattonatCast/intCast/ratCast#11499pow_lt_pow_succtoAlgebra.Order.WithZero#11507Field's fields docstrings #11508Ratinternals in the definition ofField#11639NNRat.cast#12360