Theorems · Theorem · field theory
IntermediateField.lift_rank_comap
∀ {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 : IntermediateField F E) (f : L →ₐ[F] E),
Cardinal.lift.{v, w} (Module.rank (↥(IntermediateField.comap f A)) L) = Cardinal.lift.{w, v} (A.relrank f.fieldRange)- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 2 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.
Cites13
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 · cited by 583
- Module.rankstatement · cited by 496
- AlgHom.toRingHomproof · cited by 490
- AlgHom.fieldRangestatement · cited by 57
- IntermediateField.relrankstatement · cited by 45
- IntermediateField.toSubfieldproof · cited by 38
- IntermediateField.comapstatement · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.rank_comapproof · cited by 0
- IntermediateField.finrank_comapproof · cited by 0