Theorems · Theorem · commutative algebra
Valuation.Integers.mem_of_integral
∀ {R : Type u} {Γ₀ : Type v} [inst : CommRing R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀}
{O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O R], v.Integers O → ∀ {x : R}, IsIntegral O x → x ∈ v.integer- Defined in
- Mathlib.RingTheory.Valuation.Integral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsIntegralstatement and proof · cited by 427
- Valuation.integerstatement · cited by 68
- Valuation.Integersstatement and proof · cited by 58
- Valuation.Integers.isIntegral_iff_v_le_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.Integers.integralClosureproof · cited by 1