Theorems · Theorem · commutative algebra
Localization.mk_multiset_sum
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (l : Multiset R) (b : ↥M),
Localization.mk l.sum b = (Multiset.map (fun a => Localization.mk a b) l).sum- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- AddMonoidHom.map_multiset_sumproof · cited by 10
- Localization.mkAddMonoidHomproof · cited by 4
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