Theorems · Theorem · field theory
IntermediateField.mem_lift
∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {F : IntermediateField K L}
{E : IntermediateField K ↥F} (x : ↥F), ↑x ∈ IntermediateField.lift E ↔ x ∈ E- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Subtype.val_injectiveproof · cited by 232
- Function.Injective.mem_set_imageproof · cited by 53
- IntermediateField.liftstatement · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- InfiniteGalois.restrict_fixedFieldproof · cited by 2
- IntermediateField.lift_restrictproof · cited by 2
- InfiniteGalois.restrictNormalHom_continuousproof · cited by 1
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0