Theorems · Theorem · field theory
Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable
∀ (K : Type u_1) (L : Type u_3) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [Algebra.FormallyUnramified K L] [Algebra.EssFiniteType K L] [IsPurelyInseparable K L], (algebraMap K L).range = ⊤
- Defined in
- Mathlib.RingTheory.Unramified.Field
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites79
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.rangeproof · cited by 4,705
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Cardinalproof · cited by 2,598
- TensorProductproof · cited by 2,545
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.isSeparableproof · cited by 2