Theorems · Theorem · field theory
IntermediateField.normal_iff_forall_map_le
∀ {F : Type u_1} {L : Type u_3} [inst : Field F] [inst_1 : Field L] [inst_2 : Algebra F L] [Normal F L]
{K : IntermediateField F L}, Normal F ↥K ↔ ∀ (σ : L →ₐ[F] L), IntermediateField.map σ K ≤ K- Defined in
- Mathlib.FieldTheory.Normal.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AlgHomstatement and proof · cited by 3,236
- IntermediateFieldstatement and proof · cited by 988
- Normalstatement and proof · cited by 92
- IntermediateField.mapstatement and proof · cited by 62
- iSup_le_iffproof · cited by 45
- IntermediateField.normal_iff_normalClosure_leproof · cited by 3
- IntermediateField.normalClosure_def'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.isGaloisproof · cited by 13
- IntermediateField.normal_iff_forall_map_eqproof · cited by 1