Theorems · Theorem · commutative algebra
Localization.mk_sum
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {ι : Type u_4} (f : ι → R) (s : Finset ι) (b : ↥M),
Localization.mk (∑ i ∈ s, f i) b = ∑ i ∈ s, Localization.mk (f i) b- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finset.sumstatement · cited by 5,195
- Submonoidstatement and proof · cited by 3,086
- map_sumproof · cited by 455
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- Localization.mkAddMonoidHomproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1