Theorems · Theorem · commutative algebra
LocalSubring.exists_le_valuationSubring
∀ {K : Type u_3} [inst : Field K] (A : LocalSubring K), ∃ B, A ≤ B.toLocalSubring[Stacks Tag 00IA](https://stacks.math.columbia.edu/tag/00IA)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- iSupproof · cited by 2,415
- IsUnitproof · cited by 1,602
- le_rflproof · cited by 1,558
- Set.Iciproof · cited by 1,070
- IsMaxproof · cited by 372
- Directedproof · cited by 213
- le_iSupproof · cited by 207
- ValuationSubringstatement and proof · cited by 187
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.image_subset_nonunits_valuationSubringproof · cited by 2
- IsLocalRing.exists_factor_valuationRingproof · cited by 1