Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn

∀ {K : Type u_3} [inst : Field K] {x : K} {R : Subring K},
  x ∉ R → ∀ [IsIntegrallyClosedIn (↥R) K], ∃ V, R ≤ V.toSubring ∧ x ∉ V

[Stacks Tag 090P](https://stacks.math.columbia.edu/tag/090P) (part (1))

Defined in: Mathlib.RingTheory.Valuation.LocalSubring
Cited by: 1 results in Mathlib
Foundations: Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field IsIntegrallyClosedIn

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