Theorems · Theorem · field theory
Field.finSepDegree_eq_of_equiv
∀ (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] (i : E ≃ₐ[F] K), Field.finSepDegree F E = Field.finSepDegree F K
If E and K are isomorphic as F-algebras, then they have the same Field.finSepDegree
over F.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 183 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
- AlgEquivstatement and proof · cited by 1,681
- Nat.card_congrproof · cited by 133
- Field.finSepDegreestatement · cited by 24
- Field.embEquivOfEquivproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.finSepDegree_botproof · cited by 2
- IntermediateField.finSepDegree_topproof · cited by 2
- IntermediateField.finSepDegree_bot'proof · cited by 0