Theorems · Theorem · field theory
Algebra.IsSeparable.trans
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K] [inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K] [Algebra.IsSeparable F E] [Algebra.IsSeparable E K], Algebra.IsSeparable F K
If E / F and K / E are both separable extensions, then K / F is also separable.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- Algebra.IsSeparablestatement and proof · cited by 210
- Algebra.IsSeparable.isSeparableproof · cited by 30
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.isSeparable_adjoin_pair_of_isSeparableproof · cited by 0