[Merged by Bors] - feat: Injectivity of monoid localization #9531
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Spaces and so on
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Note that I do not really know how to use the review interface properly and some of the diffs above are not correct. |
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Changed simp to simp_rw
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I have the impression you really like to make a lot of intermediate statement using -- The hypothesis `h` gives that `f` (so, `g`) is injective, and we can cancel out `b.1`.
have : b.1 * (y.1 * x.2) = b.1 * (x.1 * y.2) :=
(LocalizationMap.toMap_injective_iff fl).mpr h this
rw [mul_comm, ← IsLeftCancelMulZero.mul_left_cancel_of_ne_zero b1ne0 this, mul_comm] |
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Another stylistic comment: I think |
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Changed the proof acording to suggerences
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Adds two results on the Localization for CommMonoids: one, describes exactly when the localization map is injective, the other essentially says that the localization of a cancellative Monoid is cancellative if the localization is injective. Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com>
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| [IsCancelMulZero M] (h : ∀ ⦃x⦄, x ∈ S → IsRegular x): IsCancelMulZero N := by | ||
| have:IsLeftCancelMulZero N:= |
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lacking some spaces here; maybe fix in your next PR
[IsCancelMulZero M] (h : ∀ ⦃x⦄, x ∈ S → IsRegular x) : IsCancelMulZero N := by
have : IsLeftCancelMulZero N :=
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Adds two results on the Localization for CommMonoids: one, describes exactly when the localization map is injective, the
other essentially says that the localization of a cancellative Monoid is cancellative if the localization is injective.