Theorems · Theorem · commutative algebra
Valuation.leSubmodule_zero
∀ {Γ₀ : Type v} [inst : LinearOrderedCommGroupWithZero Γ₀] (K : Type u_1) [inst_1 : Field K] (v : Valuation K Γ₀),
v.leSubmodule 0 = ⊥- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Submodule.extproof · cited by 204
- Valuation.integerstatement and proof · cited by 68
- Valuation.leSubmodulestatement · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.leSubmodule_v_le_of_memproof · cited by 1