Theorems · Theorem · field theory
mem_separableClosure_iff
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
x ∈ separableClosure F E ↔ IsSeparable F xAn element is contained in the separable closure of F in E if and only if
it is a separable element.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 988
- IsSeparablestatement · cited by 68
- separableClosurestatement · cited by 55
Cited by7
Results whose statement or proof uses this declaration.
- separableClosure.eq_top_iffproof · cited by 6
- separableClosure.separableClosure_eq_botproof · cited by 3
- separableClosure.eq_bot_of_isPurelyInseparableproof · cited by 3
- separableClosure_leproof · cited by 2
- separableClosure.map_eq_of_separableClosure_eq_botproof · cited by 2
- IsSepClosed.separableClosure_eq_bot_iffproof · cited by 1
- separableClosure.eq_bot_iffproof · cited by 1