Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.addVal_def
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] (r : R) (u : Rˣ)
{ϖ : R}, Irreducible ϖ → ∀ (n : ℕ), r = ↑u * ϖ ^ n → (IsDiscreteValuationRing.addVal R) r = ↑n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Unitsstatement and proof · cited by 2,804
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
- Irreduciblestatement and proof · cited by 496
- emultiplicityproof · cited by 156
- IsDiscreteValuationRingstatement and proof · cited by 117
- AddValuationstatement and proof · cited by 96
- Associated.symmproof · cited by 87
Cited by3
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.addVal_uniformizerproof · cited by 6
- IsDiscreteValuationRing.addVal_eq_zero_of_unitproof · cited by 4
- IsDiscreteValuationRing.addVal_def'proof · cited by 1