Theorems · Theorem · commutative algebra
HomogeneousLocalization.eq_num_div_den
∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A] {𝒜 : ι → σ} {x : Submonoid A}
(f : HomogeneousLocalization 𝒜 x), f.val = Localization.mk f.num ⟨f.den, ⋯⟩- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- Localizationstatement · cited by 270
- Localization.mkstatement · cited by 110
- HomogeneousLocalizationstatement and proof · cited by 69
- HomogeneousLocalization.valstatement and proof · cited by 51
- Quotient.out_eq'proof · cited by 35
- HomogeneousLocalization.denstatement · cited by 5
- HomogeneousLocalization.numstatement · cited by 4
- HomogeneousLocalization.den_memstatement · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.den_smul_valproof · cited by 1