Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.intValuation_maximalIdeal
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : IsDiscreteValuationRing A] (x : A),
(IsDiscreteValuationRing.maximalIdeal A).intValuation x =
(ENat.recTopCoe 0 (fun x => ↑(Multiplicative.ofAdd ↑x)) ((IsDiscreteValuationRing.addVal A) x))⁻¹- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- Equivstatement · cited by 8,337
- ENatstatement · cited by 4,985
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Unitsproof · cited by 2,804
- zero_addproof · cited by 2,366
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- map_zeroproof · cited by 1,614
- map_mulproof · cited by 1,137
Cited by3
Results whose statement or proof uses this declaration.
- Ring.ordFrac_eq_inverse_comp_valuationproof · cited by 2
- Ring.ordMonoidWithZeroHom_eq_intValuationproof · cited by 1
- Ring.ordFrac_irreducibleproof · cited by 0