Theorems · Theorem · field theory
IntermediateField.normal_iff_normalClosure_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 ↔ IntermediateField.normalClosure F (↥K) L ≤ K- Defined in
- Mathlib.FieldTheory.Normal.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IntermediateFieldstatement and proof · cited by 988
- Normalstatement and proof · cited by 92
- LE.le.ge_iff_eq'proof · cited by 50
- IntermediateField.normalClosurestatement · cited by 38
- IntermediateField.le_normalClosureproof · cited by 8
- IntermediateField.normal_iff_normalClosure_eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.normal_iff_forall_map_leproof · cited by 2
- IntermediateField.normal_iff_forall_map_le'proof · cited by 1
- IntermediateField.normal_iff_forall_fieldRange_leproof · cited by 1