Theorems · Theorem · field theory

Field.finInsepDegree_top_le_finInsepDegree_of_isScalarTower

∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type v) [inst_3 : Field K]
  [inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K] [Module.Finite F K],
  Field.finInsepDegree E K ≤ Field.finInsepDegree F K

Defined in: Mathlib.FieldTheory.SeparableClosure
Cited by: 1 results in Mathlib
Foundations: Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Field Algebra Algebra IsScalarTower Module.Finite

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Cites13

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
Module.Finitestatement and proof · cited by 1,032
AlgHom.toRingHomproof · cited by 490
RingHom.toAlgebraproof · cited by 337
IsScalarTower.of_algebraMap_eq'proof · cited by 101
IntermediateField.restrictScalarsproof · cited by 66
separableClosureproof · cited by 55
IntermediateField.inclusionproof · cited by 32
Field.finInsepDegreestatement · cited by 15
Module.finrank_top_le_finrank_of_isScalarTowerproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

IntermediateField.finInsepDegree_le_of_left_leproof · cited by 0