Theorems · Definition · field theory

IsPurelyInseparable.HasExponent.casesOn

{K : Type u_2} →
  {L : Type u_3} →
    [inst : CommRing K] →
      [inst_1 : Ring L] →
        [inst_2 : Algebra K L] →
          {motive : IsPurelyInseparable.HasExponent K L → Sort u} →
            (t : IsPurelyInseparable.HasExponent K L) →
              ((has_exponent : ∃ e, ∀ (a : L), a ^ ringExpChar K ^ e ∈ (algebraMap K L).range) → motive ⋯) → motive t

Defined in: Mathlib.FieldTheory.PurelyInseparable.Exponent
Cited by: 1 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Ring Algebra

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Cites8

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
Ringstatement and proof · cited by 7,463
Algebra.algebraMapstatement and proof · cited by 4,706
Subringstatement · cited by 602
RingHom.rangestatement and proof · cited by 138
ringExpCharstatement and proof · cited by 27
IsPurelyInseparable.HasExponentstatement and proof · cited by 13

Cited by1

Results whose statement or proof uses this declaration.

IsPurelyInseparable.hasExponent_iffproof · cited by 1