Theorems · Definition · field theory

IsAlgClosure.casesOn

{R : Type u} →
  {K : Type v} →
    [inst : CommRing R] →
      [inst_1 : Field K] →
        [inst_2 : Algebra R K] →
          [inst_3 : Module.IsTorsionFree R K] →
            {motive : IsAlgClosure R K → Sort u_1} →
              (t : IsAlgClosure R K) →
                ((isAlgClosed : IsAlgClosed K) → (isAlgebraic : Algebra.IsAlgebraic R K) → motive ⋯) → motive t

Defined in: Mathlib.FieldTheory.IsAlgClosed.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 48 from the axioms · uses propext, Quot.sound
Assumes: CommRing Field Algebra Module.IsTorsionFree

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Module.IsTorsionFreestatement and proof · cited by 600
Algebra.IsAlgebraicstatement and proof · cited by 322
IsAlgClosedstatement and proof · cited by 150
IsAlgClosurestatement and proof · cited by 16

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.