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Theorems · Theorem · commutative algebra

Valuation.vlt_iff_lt

∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_2} [inst_2 : LinearOrderedCommMonoidWithZero Γ₀]
  (v : Valuation R Γ₀) [v.Compatible] {x y : R}, x <ᵥ y ↔ v x < v y
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext
Assumes
RingValuativeRelLinearOrderedCommMonoidWithZeroValuation.Compatible
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Valuation.vlt_one_iff · cited by 0Valuation.vlt_one_iffValuation.one_vlt_iff · cited by 0Valuation.one_vlt_iffDFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingValuation · cited by 823ValuationValuativeRel · cited by 241ValuativeRelLinearOrderedCommMonoidWithZero · cited by 139LinearOrderedCommMonoidWi…Valuation.Compatible · cited by 71Valuation.CompatibleValuativeRel.vlt · cited by 49ValuativeRel.vltValuation.vlt_iff_ltCITED BYCITES

Cites7

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Cited by2

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