Theorems · Theorem · commutative algebra
Valuation.ltIdeal_le_leIdeal
∀ {R : Type u} {Γ₀ : Type v} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
(γ : Γ₀ˣ), v.ltIdeal γ ≤ v.leIdeal ↑γ- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- Unitsstatement and proof · cited by 2,804
- LT.lt.leproof · cited by 2,189
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.integerstatement and proof · cited by 68
- Valuation.leIdealstatement · cited by 7
- Valuation.ltIdealstatement and proof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.ltIdeal_v_le_of_memproof · cited by 0