Theorems · Theorem · field theory
Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_le
∀ {E : Type v} [inst : Field E] {L : Type w} [inst_1 : Field L] (A B : Subfield E) (f : L →+* E),
B ≤ f.fieldRange →
Cardinal.lift.{v, w} ((Subfield.comap f A).relrank (Subfield.comap f B)) = Cardinal.lift.{w, v} (A.relrank B)- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Cardinalstatement · cited by 2,598
- Cardinal.liftstatement and proof · cited by 583
- Subfieldstatement and proof · cited by 303
- inf_of_le_leftproof · cited by 186
- RingHom.fieldRangestatement and proof · cited by 40
- Subfield.relrankstatement and proof · cited by 40
- Subfield.comapstatement and proof · cited by 29
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_infproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_surjectiveproof · cited by 2
- Subfield.relrank_comap_comap_eq_relrank_of_leproof · cited by 0
- Subfield.relfinrank_comap_comap_eq_relfinrank_of_leproof · cited by 0