Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.addVal_eq_top_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {a : R},
(IsDiscreteValuationRing.addVal R) a = ⊤ ↔ a = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Unitsproof · cited by 2,804
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- Irreducibleproof · cited by 496
- Associatedproof · cited by 296
- IsDiscreteValuationRingstatement and proof · cited by 117
- AddValuationstatement · cited by 96
Cited by4
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iffproof · cited by 1
- IsDiscreteValuationRing.addVal_le_iff_dvdproof · cited by 1
- IsDiscreteValuationRing.toWithBotNat_eq_bot_iffproof · cited by 0
- IsDiscreteValuationRing.addVal_eq_iff_associatedproof · cited by 0