Theorems · Theorem · commutative algebra

Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing

∀ {F : Type u} {Γ₀ : Type v} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation F Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O F] [IsPrincipalIdealRing O],
  v.Integers O → ¬DenselyOrdered ↑(Set.range ⇑v)

Defined in: Mathlib.RingTheory.Valuation.Integers
Cited by: 1 results in Mathlib
Foundations: Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrderedCommGroupWithZero CommRing Algebra IsPrincipalIdealRing

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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
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
SetLike.coeproof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Set.Elemstatement and proof · cited by 7,166
Set.preimageproof · cited by 4,946
Idealproof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Set.rangestatement and proof · cited by 4,705
LT.lt.leproof · cited by 2,189

Cited by1

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Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrderedproof · cited by 1