Theorems · Theorem · field theory
IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_le
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {L : Type w} [inst_3 : Field L]
[inst_4 : Algebra F L] (A B : IntermediateField F E) (f : L →ₐ[F] E),
B ≤ f.fieldRange →
Cardinal.lift.{v, w} ((IntermediateField.comap f A).relrank (IntermediateField.comap f B)) =
Cardinal.lift.{w, v} (A.relrank B)- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AlgHomstatement and proof · cited by 3,236
- Cardinalstatement · cited by 2,598
- IntermediateFieldstatement and proof · cited by 988
- Cardinal.liftstatement and proof · cited by 583
- inf_of_le_leftproof · cited by 186
- AlgHom.fieldRangestatement and proof · cited by 57
- IntermediateField.relrankstatement and proof · cited by 45
- IntermediateField.comapstatement and proof · cited by 25
- IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_infproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_surjectiveproof · cited by 2
- IntermediateField.relrank_comap_comap_eq_relrank_of_leproof · cited by 0
- IntermediateField.relfinrank_comap_comap_eq_relfinrank_of_leproof · cited by 0