Theorems · Theorem · field theory
Field.rank_mul_sepDegree_of_isSeparable
∀ (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] [Algebra.IsSeparable F E], Module.rank F E * Field.sepDegree E K = Field.sepDegree F K
The same-universe version of Field.lift_rank_mul_lift_sepDegree_of_isSeparable.
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- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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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 · cited by 2,598
- Module.rankstatement and proof · cited by 496
- Algebra.IsSeparablestatement and proof · cited by 210
- Cardinal.lift_idproof · cited by 163
- Field.sepDegreestatement and proof · cited by 24
- Field.lift_rank_mul_lift_sepDegree_of_isSeparableproof · cited by 2
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