Theorems · Definition · commutative algebra

Algebra.IsStandardSmooth.casesOn

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          {motive : Algebra.IsStandardSmooth R S → Sort u_1} →
            (t : Algebra.IsStandardSmooth R S) →
              ((out : ∃ ι σ, ∃ (x : Finite σ), Finite ι ∧ Nonempty (Algebra.SubmersivePresentation R S ι σ)) →
                  motive ⋯) →
                motive t

Defined in

Mathlib.RingTheory.Smooth.StandardSmooth

Cited by

4 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

CommRingCommRingAlgebra