Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iff
∀ {R : Type u_2} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {x y : R},
x ≠ 0 → y ≠ 0 → (IsDiscreteValuationRing.toWithBotNat x ≤ IsDiscreteValuationRing.toWithBotNat y ↔ x ∣ y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Top.topproof · cited by 9,680
- ENatproof · cited by 4,985
- IsDomainstatement and proof · cited by 2,196
- WithBotstatement · cited by 1,498
- IsDiscreteValuationRingstatement and proof · cited by 117
- WithBot.coe_le_coeproof · cited by 76
- ENat.recTopCoeproof · cited by 75
- WithTop.coe_le_coeproof · cited by 65
- IsDiscreteValuationRing.addValproof · cited by 22
- IsDiscreteValuationRing.toWithBotNatstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.dvd_of_toWithBotNat_le_toWithBotNatproof · cited by 0