Theorems · Theorem · field theory
Field.isSeparable_inv
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
IsSeparable F x → IsSeparable F x⁻¹If x is a separable element, then x⁻¹ is also a separable element.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IntermediateField.adjoinproof · cited by 382
- IsSeparablestatement and proof · cited by 68
- IntermediateField.mem_adjoin_simple_selfproof · cited by 19
- IntermediateField.isSeparable_of_mem_isSeparableproof · cited by 7
- IntermediateField.inv_memproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- separableClosureproof · cited by 55