Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.addVal_le_iff_dvd
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {a b : R},
(IsDiscreteValuationRing.addVal R) a ≤ (IsDiscreteValuationRing.addVal R) b ↔ a ∣ b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- ENatstatement and proof · cited by 4,985
- IsDomainstatement and proof · cited by 2,196
- Associatedproof · cited by 296
- Primeproof · cited by 277
- top_le_iffproof · cited by 175
- emultiplicityproof · cited by 156
- Dvd.dvd.transproof · cited by 148
- IsDiscreteValuationRingstatement and proof · cited by 117
- AddValuationstatement and proof · cited by 96
- Associated.symmproof · cited by 87
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iffproof · cited by 1