Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.adicCompletion.casesOn

{R : Type u_1} →
  [inst : CommRing R] →
    [inst_1 : IsDedekindDomain R] →
      {K : Type u_2} →
        [inst_2 : Field K] →
          [inst_3 : Algebra R K] →
            [inst_4 : IsFractionRing R K] →
              {v : IsDedekindDomain.HeightOneSpectrum R} →
                {motive : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v → Sort u} →
                  (t : IsDedekindDomain.HeightOneSpectrum.adicCompletion K v) →
                    ((toCompletion : (IsDedekindDomain.HeightOneSpectrum.valuation K v).Completion) →
                        motive { toCompletion := toCompletion }) →
                      motive t

Defined in

Mathlib.RingTheory.DedekindDomain.AdicValuation

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainFieldAlgebraIsFractionRing