Theorems · Theorem · field theory
IsGalois.of_fixedField_eq_bot
∀ (F : Type u_1) [inst : Field F] (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E], IntermediateField.fixedField ⊤ = ⊥ → IsGalois F E
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 145 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
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- IsGaloisstatement and proof · cited by 149
- IntermediateField.fixedFieldstatement and proof · cited by 25
- isGalois_iff_isGalois_botproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsGalois.tfaeproof · cited by 2
- IsGalois.of_card_aut_eq_finrankproof · cited by 1