Theorems · Theorem · field theory
Field.insepDegree_eq_of_isSeparable
∀ (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], Field.insepDegree F K = Field.insepDegree E K
If K / E / F is a field extension tower, such that E / F is separable,
then $[K:F]_i = [K:E]_i$.
It is a special case of Field.lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic, and is an
intermediate result used to prove it.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Cardinalstatement and proof · cited by 2,598
- IntermediateFieldproof · cited by 988
- Module.rankproof · cited by 496
- Algebra.IsSeparablestatement and proof · cited by 210
- IntermediateField.restrictScalarsproof · cited by 66
- separableClosureproof · cited by 55
- Field.insepDegreestatement and proof · cited by 23
- separableClosure.eq_restrictScalars_of_isSeparableproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Field.lift_insepDegree_mul_lift_insepDegree_of_isAlgebraicproof · cited by 2