Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.HasCoeffs.casesOn

{R : Type u_1} →
  {S : Type u_2} →
    {ι : Type u_3} →
      {σ : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : Finite σ] →
                {P : Algebra.SubmersivePresentation R S ι σ} →
                  {R₀ : Type u_5} →
                    [inst_4 : CommRing R₀] →
                      [inst_5 : Algebra R₀ R] →
                        [inst_6 : Algebra R₀ S] →
                          [inst_7 : IsScalarTower R₀ R S] →
                            {motive : P.HasCoeffs R₀ → Sort u} →
                              (t : P.HasCoeffs R₀) →
                                ((coeffs_subset_range : P.coeffs ⊆ ↑(algebraMap R₀ R).range) → motive ⋯) → motive t

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

0 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteCommRingAlgebraAlgebraIsScalarTower