Theorems · Definition · commutative algebra

IsRegularLocalRing.casesOn

{R : Type u_1} →
  [inst : CommRing R] →
    {motive : IsRegularLocalRing R → Sort u} →
      (t : IsRegularLocalRing R) →
        ([toIsLocalRing : IsLocalRing R] →
            [toIsNoetherian : IsNoetherian R R] →
              (spanFinrank_maximalIdeal : ↑(Submodule.spanFinrank (IsLocalRing.maximalIdeal R)) = ringKrullDim R) →
                motive ⋯) →
          motive t

Defined in: Mathlib.RingTheory.RegularLocalRing.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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CommRingstatement and proof · cited by 17,173
ENatstatement · cited by 4,985
WithBotstatement · cited by 1,498
IsLocalRingstatement and proof · cited by 339
IsLocalRing.maximalIdealstatement and proof · cited by 297
IsNoetherianstatement and proof · cited by 208
ringKrullDimstatement and proof · cited by 75
Submodule.spanFinrankstatement and proof · cited by 49
IsRegularLocalRingstatement and proof · cited by 8

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