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feat(algebra/field/basic): nnrat.cast
#16554
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YaelDillies
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@semorrison, here is the source of my splitting ideas. Basically it's:
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src/algebra/group_power/lemmas.lean
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The changes to this file are unrelated cleanup, right?
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| @@ -143,6 +143,8 @@ alias even.zpow_pos_iff ↔ _ even.zpow_pos | |||
| alias odd.zpow_neg_iff ↔ _ odd.zpow_neg | |||
| alias odd.zpow_nonpos_iff ↔ _ odd.zpow_nonpos | |||
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| @[simp] lemma abs_zpow (a : α) (n : ℤ) : |a ^ n| = |a| ^ n := map_zpow₀ (abs_hom : α →*₀ α) a n | |||
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This feels like a weird place for this lemma; do we have abs_inv and abs_div already that it could go next to?
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We do have the lemmas in algebra.order.field.basic, but map_zpow₀ isn't available there. Also note that algebra.order.field.power is precisely about zpow and nothing else.
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Ah, in which case I'll reduce my comment to "surely this doesn't belong in this PR"!
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…ditive monoids While many of the lemmas cease to apply, the definitions of sequences and their sums are still perfectly well-behaved in additive monoids; no negation is needed. We could use this to generalize `NormedSpace.exp` such that it works with `NNReal`, but unless leanprover-community/mathlib3#16554 or similar lands and provides a `DivisionSemiring.nnqsmul` field, that would conflict with #8370.
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Redone in leanprover-community/mathlib4#11203. |
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Define the canonical coercion
ℚ≥0 → αwhereαis adivision_semiring. This involves a lot of import shuffling.The new fields are
ringandfieldinstances #17348int.castinstead ofrat.of_int#17392pow_minus_two_nonneg#18591floor_ringfromfield#18596divlemmas #18607