Theorems · Theorem · field theory
IntermediateField.isSeparable_of_mem_isSeparable
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {L : IntermediateField F E}
[Algebra.IsSeparable F ↥L] {x : E}, x ∈ L → IsSeparable F x- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 117 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
- Algebra.IsSeparablestatement and proof · cited by 210
- Polynomial.Separableproof · cited by 117
- IsSeparablestatement · cited by 68
- Algebra.IsSeparable.isSeparableproof · cited by 30
- IntermediateField.minpoly_eqproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- IntermediateField.isSeparable_adjoin_simple_iff_isSeparableproof · cited by 4
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- Field.isSeparable_subproof · cited by 1
- Field.isSeparable_mulproof · cited by 0
- Field.isSeparable_negproof · cited by 0
- Field.isSeparable_addproof · cited by 0
- Field.isSeparable_invproof · cited by 0