Theorems · Theorem · commutative algebra
Valuation.leIdeal_v_le_of_mem
∀ {Γ₀ : Type v} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_1} [inst_1 : Field K] (v : Valuation K Γ₀)
{I : Ideal ↥v.integer} {x : ↥v.integer}, x ∈ I → v.leIdeal (v ↑x) ≤ I- Defined in
- Mathlib.RingTheory.Valuation.Integers
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- map_zeroproof · cited by 1,614
- eq_or_neproof · cited by 1,117
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Iff.notproof · cited by 489
- zero_leproof · cited by 382
- Submodule.smul_memproof · cited by 204
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.ltIdeal_v_le_of_memproof · cited by 0