Theorems · Definition · commutative algebra

IsRegularRing.casesOn

{R : Type u_2} →
  [inst : CommRing R] →
    {motive : IsRegularRing R → Sort u} →
      (t : IsRegularRing R) →
        ([toIsNoetherian : IsNoetherian R R] →
            (isRegularLocalRing_localization :
                ∀ (p : Ideal R) [inst_1 : p.IsPrime], IsRegularLocalRing (Localization.AtPrime p)) →
              motive ⋯) →
          motive t

Defined in: Mathlib.RingTheory.RegularLocalRing.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 44 from the axioms · uses propext, Quot.sound
Assumes: CommRing

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CommRingstatement and proof · cited by 17,173
Idealstatement and proof · cited by 4,748
Ideal.IsPrimestatement and proof · cited by 827
Ideal.primeComplstatement · cited by 462
Localization.AtPrimestatement and proof · cited by 299
IsNoetherianstatement and proof · cited by 208
IsRegularLocalRingstatement and proof · cited by 8
IsRegularRingstatement and proof · cited by 3

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