Theorems · Theorem · commutative algebra
Valuation.ltSubmodule_le_leSubmodule
∀ {R : Type u} {Γ₀ : Type v} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
(γ : Γ₀ˣ), v.ltSubmodule γ ≤ v.leSubmodule ↑γ- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 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
- Submodulestatement · cited by 7,192
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.integerstatement · cited by 68
- Valuation.leSubmodulestatement · cited by 7
- Valuation.ltSubmodulestatement · cited by 4
- Valuation.ltAddSubgroup_le_leAddSubgroupproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.ltSubmodule_v_le_of_memproof · cited by 0