Theorems · Theorem · field theory
IntermediateField.finInsepDegree_le_of_left_le
∀ {F : Type u} [inst : Field F] {K : Type v} [inst_1 : Field K] [inst_2 : Algebra F K] {E₁ E₂ : IntermediateField F K},
E₁ ≤ E₂ → ∀ [Module.Finite (↥E₁) K], Field.finInsepDegree (↥E₂) K ≤ Field.finInsepDegree (↥E₁) K- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerproof · cited by 3,896
- Module.Finitestatement and proof · cited by 1,032
- IntermediateFieldstatement and proof · cited by 988
- AlgHom.toRingHomproof · cited by 490
- RingHom.toAlgebraproof · cited by 337
- IsScalarTower.of_algebraMap_eq'proof · cited by 101
- IntermediateField.inclusionproof · cited by 32
- Field.finInsepDegreestatement · cited by 15
- Field.finInsepDegree_top_le_finInsepDegree_of_isScalarTowerproof · cited by 1
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