Theorems · Definition · commutative algebra
IsDiscreteValuationRing.toWithBotNat
{R : Type u_2} → [inst : CommRing R] → [inst_1 : IsDomain R] → [IsDiscreteValuationRing R] → R → WithBot ℕA modification of the valuation, sending 0 to ⊥ instead of ⊤.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsDomainstatement and proof · cited by 2,196
- WithBotstatement · cited by 1,498
- IsDiscreteValuationRingstatement and proof · cited by 117
- IsDiscreteValuationRing.addValproof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.toWithBotNat.congr_simpstatement and proof · cited by 1
- IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iffstatement · cited by 1
- IsDiscreteValuationRing.toWithBotNat_zerostatement · cited by 1
- IsDiscreteValuationRing.dvd_of_toWithBotNat_le_toWithBotNatstatement and proof · cited by 0
- IsDiscreteValuationRing.toEuclideanDomainproof · cited by 0
- IsDiscreteValuationRing.toWithBotNat_eq_bot_iffstatement · cited by 0
- IsDiscreteValuationRing.bot_lt_toWithBotNat_iffstatement · cited by 0