Theorems · Definition · field theory

IntermediateField.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} → IntermediateField K ↥F → IntermediateField K L

Lift an intermediate field of an intermediate field.

Defined in: Mathlib.FieldTheory.IntermediateField.Basic
Cited by: 22 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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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 and proof · cited by 988
IntermediateField.mapproof · cited by 62
IntermediateField.valproof · cited by 42

Cited by23

Results whose statement or proof uses this declaration.

IntermediateField.lift_topstatement · cited by 6
IntermediateField.lift_adjoinstatement · cited by 5
IntermediateField.mem_liftstatement · cited by 4
IntermediateField.liftAlgEquivstatement and proof · cited by 4
IntermediateField.lift_injectivestatement · cited by 3
IntermediateField.lift_lestatement and proof · cited by 3
InfiniteGalois.restrict_fixedFieldstatement and proof · cited by 2
IntermediateField.LinearDisjoint.of_inf_eq_botproof · cited by 2
IntermediateField.lift_injstatement · cited by 2
IntermediateField.lift_restrictstatement and proof · cited by 2
InfiniteGalois.normal_iff_isGaloisproof · cited by 2
InfiniteGalois.restrictNormalHom_continuousproof · cited by 1