Theorems · Theorem · group theory
Localization.mk_prod
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {ι : Type u_4} (t : Finset ι) (f : ι → M) (s : ι → ↥S),
∏ i ∈ t, Localization.mk (f i) (s i) = Localization.mk (∏ i ∈ t, f i) (∏ i ∈ t, s i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Submonoidstatement and proof · cited by 3,086
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Localizationstatement · cited by 270
- Finset.induction_onproof · cited by 167
- Localization.mkstatement and proof · cited by 110
- Finset.prod_insertproof · cited by 109
- Localization.mk_mulproof · cited by 12
- Localization.mk_oneproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1