Theorems · Theorem · commutative algebra
Localization.mk_list_sum
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (l : List R) (b : ↥M),
Localization.mk l.sum b = (List.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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- map_list_sumproof · cited by 31
- Localization.mkAddMonoidHomproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.