Theorems · Theorem · field theory
Field.isSeparable_sub
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x y : E},
IsSeparable F x → IsSeparable F y → IsSeparable F (x - y)If x and y are both separable elements, then x - y is also a separable element.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 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.subset_adjoinproof · cited by 59
- IntermediateField.isSeparable_of_mem_isSeparableproof · cited by 7
- IntermediateField.sub_memproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsKrasner.of_completeSpace_of_normalproof · cited by 0