Theorems · Theorem · commutative algebra
HomogeneousLocalization.ext_iff_val
∀ {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 g : HomogeneousLocalization 𝒜 x), f = g ↔ f.val = g.val- Cited by
- 7 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HomogeneousLocalizationstatement and proof · cited by 69
- HomogeneousLocalization.valstatement and proof · cited by 51
- HomogeneousLocalization.val_injectiveproof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMemproof · cited by 2
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_memproof · cited by 2
- HomogeneousLocalization.isUnit_iff_isUnit_valproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.add_memproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.primeproof · cited by 0
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff'proof · cited by 0
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_memproof · cited by 0