Theorems · Theorem · commutative algebra
Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v
∀ {F : Type u_1} {Γ₀ : Type u_2} {O : Type u_3} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀]
[inst_2 : CommRing O] [inst_3 : Algebra O F] {v : Valuation F Γ₀},
v.Integers O → (WfDvdMonoid O ↔ WellFounded (Function.onFun (fun x1 x2 => x1 > x2) (⇑v ∘ ⇑(algebraMap O F))))- Defined in
- Mathlib.RingTheory.Valuation.Archimedean
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 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.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- Valuationstatement and proof · cited by 823
- Function.onFunstatement and proof · cited by 570
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.Integersstatement and proof · cited by 58
- WfDvdMonoidstatement and proof · cited by 37
- wellFounded_dvdNotUnitproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrderedproof · cited by 1